Properties

Label 9450.2.a
Level 9450
Weight 2
Character orbit a
Rep. character \(\chi_{9450}(1,\cdot)\)
Character field \(\Q\)
Dimension 152
Newforms 128
Sturm bound 4320
Trace bound 17

Related objects

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Defining parameters

Level: \( N \) = \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 9450.a (trivial)
Character field: \(\Q\)
Newforms: \( 128 \)
Sturm bound: \(4320\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9450))\).

Total New Old
Modular forms 2232 152 2080
Cusp forms 2089 152 1937
Eisenstein series 143 0 143

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(8\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(10\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(10\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(10\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(10\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(10\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(10\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(11\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(8\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(12\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(11\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(12\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(8\)
Plus space\(+\)\(66\)
Minus space\(-\)\(86\)

Trace form

\(152q \) \(\mathstrut +\mathstrut 152q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(152q \) \(\mathstrut +\mathstrut 152q^{4} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 152q^{16} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut +\mathstrut 152q^{49} \) \(\mathstrut -\mathstrut 8q^{52} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 16q^{61} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 12q^{67} \) \(\mathstrut -\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 8q^{76} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut -\mathstrut 32q^{82} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 4q^{91} \) \(\mathstrut -\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 48q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9450))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 7
9450.2.a.a \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-6q^{11}-2q^{13}+\cdots\)
9450.2.a.b \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-6q^{11}+q^{13}+\cdots\)
9450.2.a.c \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{11}-5q^{13}+\cdots\)
9450.2.a.d \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{11}+q^{13}+\cdots\)
9450.2.a.e \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}-5q^{13}+\cdots\)
9450.2.a.f \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}-q^{13}+\cdots\)
9450.2.a.g \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}+q^{13}+\cdots\)
9450.2.a.h \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}+4q^{13}+\cdots\)
9450.2.a.i \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}+5q^{13}+\cdots\)
9450.2.a.j \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-2q^{11}+5q^{13}+\cdots\)
9450.2.a.k \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-q^{11}+3q^{13}+\cdots\)
9450.2.a.l \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{13}+q^{14}+\cdots\)
9450.2.a.m \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{13}+q^{14}+\cdots\)
9450.2.a.n \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{13}+q^{14}+\cdots\)
9450.2.a.o \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{13}+q^{14}+\cdots\)
9450.2.a.p \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+7q^{13}+q^{14}+\cdots\)
9450.2.a.q \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{11}-5q^{13}+\cdots\)
9450.2.a.r \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{11}+5q^{13}+\cdots\)
9450.2.a.s \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{11}-5q^{13}+\cdots\)
9450.2.a.t \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{11}+6q^{13}+\cdots\)
9450.2.a.u \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}-5q^{13}+\cdots\)
9450.2.a.v \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}+q^{13}+\cdots\)
9450.2.a.w \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+4q^{11}-6q^{13}+\cdots\)
9450.2.a.x \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+4q^{11}-q^{13}+\cdots\)
9450.2.a.y \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+6q^{11}-5q^{13}+\cdots\)
9450.2.a.z \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+6q^{11}+4q^{13}+\cdots\)
9450.2.a.ba \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-6q^{11}+5q^{13}+\cdots\)
9450.2.a.bb \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-5q^{11}+5q^{13}+\cdots\)
9450.2.a.bc \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-4q^{11}-3q^{13}+\cdots\)
9450.2.a.bd \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-4q^{11}+q^{13}+\cdots\)
9450.2.a.be \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-4q^{11}+6q^{13}+\cdots\)
9450.2.a.bf \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}-6q^{13}+\cdots\)
9450.2.a.bg \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}-q^{14}+\cdots\)
9450.2.a.bh \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}+3q^{13}+\cdots\)
9450.2.a.bi \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}+5q^{13}+\cdots\)
9450.2.a.bj \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{11}-5q^{13}+\cdots\)
9450.2.a.bk \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{11}+5q^{13}+\cdots\)
9450.2.a.bl \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-7q^{13}-q^{14}+\cdots\)
9450.2.a.bm \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{13}-q^{14}+\cdots\)
9450.2.a.bn \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{13}-q^{14}+\cdots\)
9450.2.a.bo \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{13}-q^{14}+\cdots\)
9450.2.a.bp \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}-3q^{13}+\cdots\)
9450.2.a.bq \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}-3q^{13}+\cdots\)
9450.2.a.br \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}+3q^{13}+\cdots\)
9450.2.a.bs \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+2q^{11}-4q^{13}+\cdots\)
9450.2.a.bt \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}-5q^{13}+\cdots\)
9450.2.a.bu \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}-q^{13}+\cdots\)
9450.2.a.bv \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}+q^{13}+\cdots\)
9450.2.a.bw \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{11}-q^{13}+\cdots\)
9450.2.a.bx \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{11}-q^{14}+\cdots\)
9450.2.a.by \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{11}+5q^{13}+\cdots\)
9450.2.a.bz \(1\) \(75.459\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+6q^{11}+2q^{13}+\cdots\)
9450.2.a.ca \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-6q^{11}-5q^{13}+\cdots\)
9450.2.a.cb \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-6q^{11}+4q^{13}+\cdots\)
9450.2.a.cc \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-4q^{11}-6q^{13}+\cdots\)
9450.2.a.cd \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-4q^{11}-q^{13}+\cdots\)
9450.2.a.ce \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}-5q^{13}+\cdots\)
9450.2.a.cf \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}+q^{13}+\cdots\)
9450.2.a.cg \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}-5q^{13}+\cdots\)
9450.2.a.ch \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}+6q^{13}+\cdots\)
9450.2.a.ci \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-q^{11}-5q^{13}+\cdots\)
9450.2.a.cj \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-q^{11}+5q^{13}+\cdots\)
9450.2.a.ck \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-5q^{13}-q^{14}+\cdots\)
9450.2.a.cl \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-5q^{13}-q^{14}+\cdots\)
9450.2.a.cm \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{13}-q^{14}+\cdots\)
9450.2.a.cn \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{13}-q^{14}+\cdots\)
9450.2.a.co \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+7q^{13}-q^{14}+\cdots\)
9450.2.a.cp \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{11}+3q^{13}+\cdots\)
9450.2.a.cq \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{11}+5q^{13}+\cdots\)
9450.2.a.cr \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}-5q^{13}+\cdots\)
9450.2.a.cs \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}-q^{13}+\cdots\)
9450.2.a.ct \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+q^{13}+\cdots\)
9450.2.a.cu \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+4q^{13}+\cdots\)
9450.2.a.cv \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+5q^{13}+\cdots\)
9450.2.a.cw \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+5q^{11}-5q^{13}+\cdots\)
9450.2.a.cx \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+5q^{11}+q^{13}+\cdots\)
9450.2.a.cy \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+6q^{11}-2q^{13}+\cdots\)
9450.2.a.cz \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+6q^{11}+q^{13}+\cdots\)
9450.2.a.da \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-6q^{11}+2q^{13}+\cdots\)
9450.2.a.db \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-5q^{11}-q^{13}+\cdots\)
9450.2.a.dc \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-5q^{11}+q^{14}+\cdots\)
9450.2.a.dd \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-5q^{11}+5q^{13}+\cdots\)
9450.2.a.de \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{11}-5q^{13}+\cdots\)
9450.2.a.df \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{11}-q^{13}+\cdots\)
9450.2.a.dg \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{11}+q^{13}+\cdots\)
9450.2.a.dh \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-2q^{11}-4q^{13}+\cdots\)
9450.2.a.di \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{11}-3q^{13}+\cdots\)
9450.2.a.dj \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{11}-3q^{13}+\cdots\)
9450.2.a.dk \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{11}+3q^{13}+\cdots\)
9450.2.a.dl \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-7q^{13}+q^{14}+\cdots\)
9450.2.a.dm \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-2q^{13}+q^{14}+\cdots\)
9450.2.a.dn \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{13}+q^{14}+\cdots\)
9450.2.a.do \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{13}+q^{14}+\cdots\)
9450.2.a.dp \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+q^{11}-5q^{13}+\cdots\)
9450.2.a.dq \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+q^{11}+5q^{13}+\cdots\)
9450.2.a.dr \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}-6q^{13}+\cdots\)
9450.2.a.ds \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+q^{14}+\cdots\)
9450.2.a.dt \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+3q^{13}+\cdots\)
9450.2.a.du \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+5q^{13}+\cdots\)
9450.2.a.dv \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}-3q^{13}+\cdots\)
9450.2.a.dw \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}+q^{13}+\cdots\)
9450.2.a.dx \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}+6q^{13}+\cdots\)
9450.2.a.dy \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{11}+5q^{13}+\cdots\)
9450.2.a.dz \(1\) \(75.459\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+6q^{11}+5q^{13}+\cdots\)
9450.2.a.ea \(2\) \(75.459\) \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots\)
9450.2.a.eb \(2\) \(75.459\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
9450.2.a.ec \(2\) \(75.459\) \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+2\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
9450.2.a.ed \(2\) \(75.459\) \(\Q(\sqrt{73}) \) None \(-2\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.ee \(2\) \(75.459\) \(\Q(\sqrt{10}) \) None \(-2\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{11}+(-1+\cdots)q^{13}+\cdots\)
9450.2.a.ef \(2\) \(75.459\) \(\Q(\sqrt{10}) \) None \(-2\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+(2+\beta )q^{11}+\cdots\)
9450.2.a.eg \(2\) \(75.459\) \(\Q(\sqrt{10}) \) None \(-2\) \(0\) \(0\) \(2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+(-2+\beta )q^{11}+\cdots\)
9450.2.a.eh \(2\) \(75.459\) \(\Q(\sqrt{10}) \) None \(-2\) \(0\) \(0\) \(2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}+(1+\cdots)q^{13}+\cdots\)
9450.2.a.ei \(2\) \(75.459\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(0\) \(2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.ej \(2\) \(75.459\) \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(0\) \(2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.ek \(2\) \(75.459\) \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(0\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
9450.2.a.el \(2\) \(75.459\) \(\Q(\sqrt{97}) \) None \(-2\) \(0\) \(0\) \(2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+(1+\beta )q^{11}+\cdots\)
9450.2.a.em \(2\) \(75.459\) \(\Q(\sqrt{10}) \) None \(2\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}+(-1+\cdots)q^{13}+\cdots\)
9450.2.a.en \(2\) \(75.459\) \(\Q(\sqrt{10}) \) None \(2\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+(-2+\beta )q^{11}+\cdots\)
9450.2.a.eo \(2\) \(75.459\) \(\Q(\sqrt{73}) \) None \(2\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.ep \(2\) \(75.459\) \(\Q(\sqrt{6}) \) None \(2\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots\)
9450.2.a.eq \(2\) \(75.459\) \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+2\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
9450.2.a.er \(2\) \(75.459\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
9450.2.a.es \(2\) \(75.459\) \(\Q(\sqrt{97}) \) None \(2\) \(0\) \(0\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+(-1-\beta )q^{11}+\cdots\)
9450.2.a.et \(2\) \(75.459\) \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(0\) \(2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.eu \(2\) \(75.459\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.ev \(2\) \(75.459\) \(\Q(\sqrt{6}) \) None \(2\) \(0\) \(0\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
9450.2.a.ew \(2\) \(75.459\) \(\Q(\sqrt{10}) \) None \(2\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+(2+\beta )q^{11}+\cdots\)
9450.2.a.ex \(2\) \(75.459\) \(\Q(\sqrt{10}) \) None \(2\) \(0\) \(0\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+(1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9450))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9450)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(270))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(378))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(525))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(630))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(675))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(945))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1050))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1575))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1890))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4725))\)\(^{\oplus 2}\)