Properties

Label 9360.2.a
Level $9360$
Weight $2$
Character orbit 9360.a
Rep. character $\chi_{9360}(1,\cdot)$
Character field $\Q$
Dimension $120$
Newform subspaces $83$
Sturm bound $4032$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 9360 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9360.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 83 \)
Sturm bound: \(4032\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9360))\).

Total New Old
Modular forms 2064 120 1944
Cusp forms 1969 120 1849
Eisenstein series 95 0 95

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

\(2\)\(3\)\(5\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(11\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(10\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(10\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(7\)
Plus space\(+\)\(56\)
Minus space\(-\)\(64\)

Trace form

\( 120q + 4q^{7} + O(q^{10}) \) \( 120q + 4q^{7} + 8q^{11} - 8q^{17} - 8q^{19} + 8q^{23} + 120q^{25} - 24q^{29} - 8q^{31} - 16q^{37} + 8q^{41} + 8q^{43} - 20q^{47} + 120q^{49} - 8q^{53} + 24q^{61} - 4q^{67} - 16q^{71} + 24q^{73} - 8q^{77} - 28q^{83} + 16q^{85} + 24q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9360))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 13
9360.2.a.a \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}-4q^{7}+q^{13}-2q^{17}+q^{25}+\cdots\)
9360.2.a.b \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}-4q^{7}+4q^{11}+q^{13}-6q^{17}+\cdots\)
9360.2.a.c \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) \(+\) \(+\) \(+\) \(+\) \(q-q^{5}-3q^{7}-5q^{11}-q^{13}-3q^{17}+\cdots\)
9360.2.a.d \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}-3q^{7}-q^{11}-q^{13}+q^{17}+\cdots\)
9360.2.a.e \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}-3q^{7}+q^{11}+q^{13}+3q^{17}+\cdots\)
9360.2.a.f \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{5}-2q^{7}-4q^{11}-q^{13}-4q^{17}+\cdots\)
9360.2.a.g \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}-2q^{7}+q^{13}-2q^{19}-6q^{23}+\cdots\)
9360.2.a.h \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{5}-2q^{7}+4q^{11}-q^{13}-8q^{17}+\cdots\)
9360.2.a.i \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{5}-2q^{7}+4q^{11}-q^{13}-4q^{17}+\cdots\)
9360.2.a.j \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}-2q^{7}+4q^{11}-q^{13}-2q^{19}+\cdots\)
9360.2.a.k \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}-4q^{11}+q^{13}-2q^{17}+4q^{19}+\cdots\)
9360.2.a.l \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{13}-2q^{17}+8q^{19}-4q^{23}+\cdots\)
9360.2.a.m \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{5}+q^{13}+6q^{17}+8q^{19}+6q^{23}+\cdots\)
9360.2.a.n \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}+2q^{11}+q^{13}-2q^{17}-2q^{19}+\cdots\)
9360.2.a.o \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+4q^{11}+q^{13}-2q^{17}+4q^{19}+\cdots\)
9360.2.a.p \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+4q^{11}+q^{13}+6q^{17}-4q^{19}+\cdots\)
9360.2.a.q \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}+6q^{11}+q^{13}+4q^{17}-4q^{19}+\cdots\)
9360.2.a.r \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}+q^{7}-3q^{11}+q^{13}+3q^{17}+\cdots\)
9360.2.a.s \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{5}+q^{7}-q^{11}-q^{13}+5q^{17}+\cdots\)
9360.2.a.t \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}+2q^{7}-2q^{11}-q^{13}+2q^{17}+\cdots\)
9360.2.a.u \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}+2q^{7}+q^{13}+4q^{17}-6q^{19}+\cdots\)
9360.2.a.v \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}+2q^{7}+4q^{11}-q^{13}-4q^{17}+\cdots\)
9360.2.a.w \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(3\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+3q^{7}-5q^{11}+q^{13}-5q^{17}+\cdots\)
9360.2.a.x \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(3\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}+3q^{7}-3q^{11}-q^{13}+q^{17}+\cdots\)
9360.2.a.y \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(3\) \(+\) \(+\) \(+\) \(-\) \(q-q^{5}+3q^{7}+3q^{11}+q^{13}+3q^{17}+\cdots\)
9360.2.a.z \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(4\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+4q^{7}-6q^{11}+q^{13}+6q^{17}+\cdots\)
9360.2.a.ba \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(4\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}+4q^{7}+q^{13}-6q^{17}+4q^{19}+\cdots\)
9360.2.a.bb \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(-1\) \(5\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}+5q^{7}+q^{11}+q^{13}+3q^{17}+\cdots\)
9360.2.a.bc \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(-4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}-4q^{7}-q^{13}+2q^{17}-4q^{19}+\cdots\)
9360.2.a.bd \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(-3\) \(+\) \(+\) \(-\) \(+\) \(q+q^{5}-3q^{7}+5q^{11}-q^{13}+3q^{17}+\cdots\)
9360.2.a.be \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{5}-2q^{7}-4q^{11}-q^{13}+4q^{17}+\cdots\)
9360.2.a.bf \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q+q^{5}-2q^{7}-4q^{11}-q^{13}+8q^{17}+\cdots\)
9360.2.a.bg \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}-2q^{7}+q^{13}-2q^{19}-6q^{23}+\cdots\)
9360.2.a.bh \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}-2q^{7}+4q^{11}-q^{13}-8q^{17}+\cdots\)
9360.2.a.bi \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}-2q^{7}+4q^{11}-q^{13}-2q^{17}+\cdots\)
9360.2.a.bj \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{5}-2q^{7}+4q^{11}-q^{13}+4q^{17}+\cdots\)
9360.2.a.bk \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}-6q^{11}+q^{13}-4q^{17}-4q^{19}+\cdots\)
9360.2.a.bl \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}-4q^{11}-q^{13}+6q^{17}-4q^{19}+\cdots\)
9360.2.a.bm \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}-q^{13}-2q^{17}+4q^{23}+q^{25}+\cdots\)
9360.2.a.bn \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}-q^{13}+6q^{17}-4q^{23}+q^{25}+\cdots\)
9360.2.a.bo \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q+q^{5}+q^{13}-6q^{17}+8q^{19}-6q^{23}+\cdots\)
9360.2.a.bp \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{13}+6q^{17}-4q^{19}+q^{25}+\cdots\)
9360.2.a.bq \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+4q^{11}+q^{13}+2q^{17}+4q^{19}+\cdots\)
9360.2.a.br \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}-5q^{11}+q^{13}-3q^{17}+\cdots\)
9360.2.a.bs \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{5}+q^{7}+q^{11}-q^{13}-5q^{17}+\cdots\)
9360.2.a.bt \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}+3q^{11}+q^{13}-3q^{17}+\cdots\)
9360.2.a.bu \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}+q^{7}+3q^{11}+q^{13}-3q^{17}+\cdots\)
9360.2.a.bv \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+q^{7}+5q^{11}-q^{13}+7q^{17}+\cdots\)
9360.2.a.bw \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+2q^{7}-6q^{11}-q^{13}+2q^{17}+\cdots\)
9360.2.a.bx \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(3\) \(+\) \(+\) \(-\) \(-\) \(q+q^{5}+3q^{7}-3q^{11}+q^{13}-3q^{17}+\cdots\)
9360.2.a.by \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+4q^{7}-2q^{11}-q^{13}-2q^{17}+\cdots\)
9360.2.a.bz \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}+4q^{7}+q^{13}+6q^{17}+4q^{19}+\cdots\)
9360.2.a.ca \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+4q^{7}+2q^{11}-q^{13}-2q^{17}+\cdots\)
9360.2.a.cb \(1\) \(74.740\) \(\Q\) None \(0\) \(0\) \(1\) \(4\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+4q^{7}+4q^{11}+q^{13}+6q^{17}+\cdots\)
9360.2.a.cc \(2\) \(74.740\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-2\) \(-4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}-2q^{7}+(-2+\beta )q^{11}-q^{13}+\cdots\)
9360.2.a.cd \(2\) \(74.740\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(-4\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}+(-2+2\beta )q^{7}+(2-\beta )q^{11}+\cdots\)
9360.2.a.ce \(2\) \(74.740\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(-3\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}+(-1-\beta )q^{7}+(1+\beta )q^{11}-q^{13}+\cdots\)
9360.2.a.cf \(2\) \(74.740\) \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}+(-1-\beta )q^{7}+q^{13}+(-1+\beta )q^{17}+\cdots\)
9360.2.a.cg \(2\) \(74.740\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(-2\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}-\beta q^{7}+(-2+\beta )q^{11}+q^{13}+\cdots\)
9360.2.a.ch \(2\) \(74.740\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}+\beta q^{7}+2\beta q^{11}-q^{13}+(2-\beta )q^{17}+\cdots\)
9360.2.a.ci \(2\) \(74.740\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}+\beta q^{7}+(-4+\beta )q^{11}+q^{13}+\cdots\)
9360.2.a.cj \(2\) \(74.740\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(4\) \(+\) \(+\) \(+\) \(+\) \(q-q^{5}+2q^{7}-q^{13}+(2+\beta )q^{17}-2q^{19}+\cdots\)
9360.2.a.ck \(2\) \(74.740\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}+2q^{7}-3\beta q^{11}-q^{13}+(2-2\beta )q^{17}+\cdots\)
9360.2.a.cl \(2\) \(74.740\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(5\) \(-\) \(+\) \(+\) \(+\) \(q-q^{5}+(3-\beta )q^{7}+(1-\beta )q^{11}-q^{13}+\cdots\)
9360.2.a.cm \(2\) \(74.740\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(-4\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}-2q^{7}+(-3+\beta )q^{11}+q^{13}+\cdots\)
9360.2.a.cn \(2\) \(74.740\) \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(2\) \(-2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}+(-1-\beta )q^{7}+q^{13}+(1-\beta )q^{17}+\cdots\)
9360.2.a.co \(2\) \(74.740\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(2\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}-\beta q^{7}-\beta q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots\)
9360.2.a.cp \(2\) \(74.740\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(2\) \(-1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}-\beta q^{7}+(2-\beta )q^{11}+q^{13}+(4+\cdots)q^{17}+\cdots\)
9360.2.a.cq \(2\) \(74.740\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+2\beta q^{7}+(-3+\beta )q^{11}+q^{13}+\cdots\)
9360.2.a.cr \(2\) \(74.740\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+2\beta q^{7}+(1-\beta )q^{11}+q^{13}+\cdots\)
9360.2.a.cs \(2\) \(74.740\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}+(3+\beta )q^{11}-q^{13}-2q^{17}+\cdots\)
9360.2.a.ct \(2\) \(74.740\) \(\Q(\sqrt{41}) \) None \(0\) \(0\) \(2\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}+\beta q^{7}+(-2-\beta )q^{11}-q^{13}+\cdots\)
9360.2.a.cu \(2\) \(74.740\) \(\Q(\sqrt{73}) \) None \(0\) \(0\) \(2\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+\beta q^{7}+\beta q^{11}-q^{13}+\beta q^{17}+\cdots\)
9360.2.a.cv \(2\) \(74.740\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(4\) \(+\) \(+\) \(-\) \(+\) \(q+q^{5}+2q^{7}-q^{13}+(-2-\beta )q^{17}+\cdots\)
9360.2.a.cw \(2\) \(74.740\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(5\) \(-\) \(+\) \(-\) \(+\) \(q+q^{5}+(3-\beta )q^{7}+(-1+\beta )q^{11}-q^{13}+\cdots\)
9360.2.a.cx \(3\) \(74.740\) 3.3.621.1 None \(0\) \(0\) \(-3\) \(-3\) \(+\) \(+\) \(+\) \(-\) \(q-q^{5}+(-1-\beta _{2})q^{7}+(1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
9360.2.a.cy \(3\) \(74.740\) 3.3.940.1 None \(0\) \(0\) \(-3\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}-\beta _{2}q^{7}+(2+\beta _{1})q^{11}-q^{13}+\cdots\)
9360.2.a.cz \(3\) \(74.740\) 3.3.1016.1 None \(0\) \(0\) \(-3\) \(1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{5}+\beta _{2}q^{7}+(-2+\beta _{1})q^{11}-q^{13}+\cdots\)
9360.2.a.da \(3\) \(74.740\) 3.3.564.1 None \(0\) \(0\) \(-3\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+(1+\beta _{1})q^{7}+(\beta _{1}-\beta _{2})q^{11}+\cdots\)
9360.2.a.db \(3\) \(74.740\) 3.3.1849.1 None \(0\) \(0\) \(3\) \(-5\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+(-2+\beta _{1})q^{7}+(1+\beta _{2})q^{11}+\cdots\)
9360.2.a.dc \(3\) \(74.740\) 3.3.621.1 None \(0\) \(0\) \(3\) \(-3\) \(+\) \(+\) \(-\) \(-\) \(q+q^{5}+(-1-\beta _{2})q^{7}+(-1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
9360.2.a.dd \(3\) \(74.740\) 3.3.316.1 None \(0\) \(0\) \(3\) \(-1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+\beta _{1}q^{7}-\beta _{1}q^{11}+q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
9360.2.a.de \(3\) \(74.740\) 3.3.1016.1 None \(0\) \(0\) \(3\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q+q^{5}+\beta _{2}q^{7}+(2-\beta _{1})q^{11}-q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9360))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9360)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(390))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(468))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(520))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(585))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(780))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(936))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1040))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1560))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1872))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2340))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4680))\)\(^{\oplus 2}\)