Properties

Label 9702.2.a
Level $9702$
Weight $2$
Character orbit 9702.a
Rep. character $\chi_{9702}(1,\cdot)$
Character field $\Q$
Dimension $169$
Newform subspaces $107$
Sturm bound $4032$
Trace bound $31$

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Defining parameters

Level: \( N \) \(=\) \( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9702.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 107 \)
Sturm bound: \(4032\)
Trace bound: \(31\)
Distinguishing \(T_p\): \(5\), \(13\), \(17\), \(19\), \(23\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9702))\).

Total New Old
Modular forms 2080 169 1911
Cusp forms 1953 169 1784
Eisenstein series 127 0 127

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

\(2\)\(3\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(9\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(11\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(8\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(13\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(13\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(13\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(13\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(8\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(11\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(11\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(15\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(14\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(11\)
Plus space\(+\)\(74\)
Minus space\(-\)\(95\)

Trace form

\( 169q - q^{2} + 169q^{4} - 2q^{5} - q^{8} + O(q^{10}) \) \( 169q - q^{2} + 169q^{4} - 2q^{5} - q^{8} - 2q^{10} + q^{11} - 2q^{13} + 169q^{16} - 18q^{17} - 12q^{19} - 2q^{20} - q^{22} - 4q^{23} + 159q^{25} - 14q^{26} + 2q^{29} - 8q^{31} - q^{32} - 6q^{34} + 30q^{37} - 4q^{38} - 2q^{40} + 6q^{41} + 52q^{43} + q^{44} + 4q^{47} - 39q^{50} - 2q^{52} - 38q^{53} - 6q^{55} - 50q^{58} + 16q^{59} - 2q^{61} - 8q^{62} + 169q^{64} - 52q^{65} + 44q^{67} - 18q^{68} - 20q^{71} + 10q^{73} - 46q^{74} - 12q^{76} + 80q^{79} - 2q^{80} - 14q^{82} - 20q^{83} - 76q^{85} + 8q^{86} - q^{88} - 6q^{89} - 4q^{92} + 8q^{94} + 32q^{95} - 46q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9702))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7 11
9702.2.a.a \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(-4\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}-4q^{5}-q^{8}+4q^{10}-q^{11}+\cdots\)
9702.2.a.b \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(-4\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}-4q^{5}-q^{8}+4q^{10}+q^{11}+\cdots\)
9702.2.a.c \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(-3\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+q^{11}+\cdots\)
9702.2.a.d \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-q^{11}+\cdots\)
9702.2.a.e \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-q^{11}+\cdots\)
9702.2.a.f \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-q^{11}+\cdots\)
9702.2.a.g \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-q^{11}+\cdots\)
9702.2.a.h \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-q^{11}+\cdots\)
9702.2.a.i \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+q^{11}+\cdots\)
9702.2.a.j \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+q^{11}+\cdots\)
9702.2.a.k \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{11}+\cdots\)
9702.2.a.l \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{8}+q^{11}-5q^{13}+q^{16}+\cdots\)
9702.2.a.m \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{8}+q^{11}-2q^{13}+q^{16}+\cdots\)
9702.2.a.n \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{8}+q^{11}-2q^{13}+q^{16}+\cdots\)
9702.2.a.o \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{8}+q^{11}+5q^{13}+q^{16}+\cdots\)
9702.2.a.p \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{11}+\cdots\)
9702.2.a.q \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots\)
9702.2.a.r \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots\)
9702.2.a.s \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(2\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots\)
9702.2.a.t \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots\)
9702.2.a.u \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots\)
9702.2.a.v \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{11}+\cdots\)
9702.2.a.w \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(2\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{11}+\cdots\)
9702.2.a.x \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{11}+\cdots\)
9702.2.a.y \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{11}+\cdots\)
9702.2.a.z \(1\) \(77.471\) \(\Q\) None \(-1\) \(0\) \(3\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+q^{11}+\cdots\)
9702.2.a.ba \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(-4\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}+q^{11}+\cdots\)
9702.2.a.bb \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(-4\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}+q^{11}+\cdots\)
9702.2.a.bc \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-q^{11}+\cdots\)
9702.2.a.bd \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+q^{11}+\cdots\)
9702.2.a.be \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+q^{11}+\cdots\)
9702.2.a.bf \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}-q^{11}+\cdots\)
9702.2.a.bg \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}-q^{11}+\cdots\)
9702.2.a.bh \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+q^{11}+\cdots\)
9702.2.a.bi \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+q^{11}+\cdots\)
9702.2.a.bj \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-q^{11}+\cdots\)
9702.2.a.bk \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{8}-q^{11}-4q^{13}+q^{16}+\cdots\)
9702.2.a.bl \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+q^{8}-q^{11}-4q^{13}+q^{16}+\cdots\)
9702.2.a.bm \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{8}-q^{11}-2q^{13}+q^{16}+\cdots\)
9702.2.a.bn \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{8}-q^{11}+4q^{13}+q^{16}+\cdots\)
9702.2.a.bo \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{8}-q^{11}+4q^{13}+q^{16}+\cdots\)
9702.2.a.bp \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{8}+q^{11}-6q^{13}+q^{16}+\cdots\)
9702.2.a.bq \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{8}+q^{11}-4q^{13}+q^{16}+\cdots\)
9702.2.a.br \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{8}+q^{11}-q^{13}+q^{16}+\cdots\)
9702.2.a.bs \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{8}+q^{11}+q^{13}+q^{16}+\cdots\)
9702.2.a.bt \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{8}+q^{11}+2q^{13}+q^{16}+\cdots\)
9702.2.a.bu \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{8}+q^{11}+4q^{13}+q^{16}+\cdots\)
9702.2.a.bv \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{8}+q^{11}+4q^{13}+q^{16}+\cdots\)
9702.2.a.bw \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-q^{11}+\cdots\)
9702.2.a.bx \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(2\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}-q^{11}+\cdots\)
9702.2.a.by \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}-q^{11}+\cdots\)
9702.2.a.bz \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}-q^{11}+\cdots\)
9702.2.a.ca \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}+q^{11}+\cdots\)
9702.2.a.cb \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}+q^{11}+\cdots\)
9702.2.a.cc \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}+q^{11}+\cdots\)
9702.2.a.cd \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(3\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-q^{11}+\cdots\)
9702.2.a.ce \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(3\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}+q^{11}+\cdots\)
9702.2.a.cf \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(3\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}+q^{11}+\cdots\)
9702.2.a.cg \(1\) \(77.471\) \(\Q\) None \(1\) \(0\) \(4\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+4q^{5}+q^{8}+4q^{10}+q^{11}+\cdots\)
9702.2.a.ch \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-4\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+(-2+\beta )q^{5}-q^{8}+(2+\cdots)q^{10}+\cdots\)
9702.2.a.ci \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-4\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+q^{11}+\cdots\)
9702.2.a.cj \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+(-1+\beta )q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots\)
9702.2.a.ck \(2\) \(77.471\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+(-1-\beta )q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots\)
9702.2.a.cl \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}-q^{11}+\cdots\)
9702.2.a.cm \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+3\beta q^{5}-q^{8}-3\beta q^{10}+\cdots\)
9702.2.a.cn \(2\) \(77.471\) \(\Q(\sqrt{10}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+q^{11}+\cdots\)
9702.2.a.co \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{8}+q^{11}+3\beta q^{13}+\cdots\)
9702.2.a.cp \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+3\beta q^{5}-q^{8}-3\beta q^{10}+\cdots\)
9702.2.a.cq \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{8}+q^{11}-3\beta q^{13}+\cdots\)
9702.2.a.cr \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+2\beta q^{5}-q^{8}-2\beta q^{10}+\cdots\)
9702.2.a.cs \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+3\beta q^{5}-q^{8}-3\beta q^{10}+\cdots\)
9702.2.a.ct \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+q^{11}+\cdots\)
9702.2.a.cu \(2\) \(77.471\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
9702.2.a.cv \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
9702.2.a.cw \(2\) \(77.471\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
9702.2.a.cx \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(4\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}+(2+\beta )q^{5}-q^{8}+(-2+\cdots)q^{10}+\cdots\)
9702.2.a.cy \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(4\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{11}+\cdots\)
9702.2.a.cz \(2\) \(77.471\) \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+(-1+\beta )q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots\)
9702.2.a.da \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+(-1+\beta )q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots\)
9702.2.a.db \(2\) \(77.471\) \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots\)
9702.2.a.dc \(2\) \(77.471\) \(\Q(\sqrt{10}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots\)
9702.2.a.dd \(2\) \(77.471\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots\)
9702.2.a.de \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+q^{8}-q^{11}-\beta q^{13}+q^{16}+\cdots\)
9702.2.a.df \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+2\beta q^{5}+q^{8}+2\beta q^{10}+\cdots\)
9702.2.a.dg \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots\)
9702.2.a.dh \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}+q^{8}-q^{11}+3\beta q^{13}+\cdots\)
9702.2.a.di \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}+2\beta q^{5}+q^{8}+2\beta q^{10}+\cdots\)
9702.2.a.dj \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}+3\beta q^{5}+q^{8}+3\beta q^{10}+\cdots\)
9702.2.a.dk \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots\)
9702.2.a.dl \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+q^{8}-q^{11}-\beta q^{13}+q^{16}+\cdots\)
9702.2.a.dm \(2\) \(77.471\) \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots\)
9702.2.a.dn \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{8}+q^{11}-\beta q^{13}+q^{16}+\cdots\)
9702.2.a.do \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+3\beta q^{5}+q^{8}+3\beta q^{10}+\cdots\)
9702.2.a.dp \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+q^{11}+\cdots\)
9702.2.a.dq \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+q^{11}+\cdots\)
9702.2.a.dr \(2\) \(77.471\) \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+(1+\beta )q^{5}+q^{8}+(1+\beta )q^{10}+\cdots\)
9702.2.a.ds \(2\) \(77.471\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}+(1+\beta )q^{5}+q^{8}+(1+\beta )q^{10}+\cdots\)
9702.2.a.dt \(3\) \(77.471\) 3.3.621.1 None \(-3\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-\beta _{2}q^{5}-q^{8}+\beta _{2}q^{10}+\cdots\)
9702.2.a.du \(3\) \(77.471\) 3.3.621.1 None \(-3\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+\beta _{2}q^{5}-q^{8}-\beta _{2}q^{10}+\cdots\)
9702.2.a.dv \(3\) \(77.471\) 3.3.2700.1 None \(-3\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-\beta _{1}q^{5}-q^{8}+\beta _{1}q^{10}+\cdots\)
9702.2.a.dw \(3\) \(77.471\) 3.3.2700.1 None \(-3\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+\beta _{1}q^{5}-q^{8}-\beta _{1}q^{10}+\cdots\)
9702.2.a.dx \(3\) \(77.471\) 3.3.1304.1 None \(-3\) \(0\) \(2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+(1+\beta _{2})q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
9702.2.a.dy \(3\) \(77.471\) 3.3.1304.1 None \(3\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+(-1-\beta _{2})q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots\)
9702.2.a.dz \(4\) \(77.471\) 4.4.4352.1 None \(-4\) \(0\) \(-4\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}+(-1-\beta _{3})q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots\)
9702.2.a.ea \(4\) \(77.471\) 4.4.4352.1 None \(-4\) \(0\) \(4\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}+(1+\beta _{3})q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
9702.2.a.eb \(4\) \(77.471\) 4.4.14336.1 None \(4\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+\beta _{2}q^{5}+q^{8}+\beta _{2}q^{10}+\cdots\)
9702.2.a.ec \(4\) \(77.471\) 4.4.14336.1 None \(4\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+\beta _{2}q^{5}+q^{8}+\beta _{2}q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9702))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9702)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(693))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(882))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1078))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1386))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1617))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3234))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4851))\)\(^{\oplus 2}\)