Properties

Label 6762.2.a
Level $6762$
Weight $2$
Character orbit 6762.a
Rep. character $\chi_{6762}(1,\cdot)$
Character field $\Q$
Dimension $150$
Newform subspaces $74$
Sturm bound $2688$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6762.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 74 \)
Sturm bound: \(2688\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6762))\).

Total New Old
Modular forms 1376 150 1226
Cusp forms 1313 150 1163
Eisenstein series 63 0 63

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

\(2\)\(3\)\(7\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(12\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(8\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(10\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(11\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(11\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(9\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(9\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(12\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(14\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(13\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(65\)
Minus space\(-\)\(85\)

Trace form

\( 150q + 2q^{2} - 2q^{3} + 150q^{4} + 4q^{5} - 2q^{6} + 2q^{8} + 150q^{9} + O(q^{10}) \) \( 150q + 2q^{2} - 2q^{3} + 150q^{4} + 4q^{5} - 2q^{6} + 2q^{8} + 150q^{9} - 2q^{12} - 4q^{13} - 4q^{15} + 150q^{16} - 4q^{17} + 2q^{18} - 12q^{19} + 4q^{20} - 12q^{22} - 2q^{24} + 146q^{25} + 12q^{26} - 2q^{27} - 4q^{29} - 16q^{31} + 2q^{32} + 4q^{33} + 12q^{34} + 150q^{36} + 32q^{37} - 8q^{38} + 36q^{39} - 12q^{41} + 60q^{43} + 4q^{45} + 4q^{46} - 24q^{47} - 2q^{48} + 86q^{50} + 8q^{51} - 4q^{52} + 76q^{53} - 2q^{54} + 16q^{55} + 60q^{57} + 68q^{58} + 8q^{59} - 4q^{60} + 24q^{61} + 8q^{62} + 150q^{64} + 40q^{65} + 20q^{67} - 4q^{68} - 4q^{69} - 40q^{71} + 2q^{72} + 12q^{73} + 52q^{74} + 2q^{75} - 12q^{76} - 4q^{78} + 4q^{80} + 150q^{81} - 4q^{82} + 24q^{83} + 72q^{85} - 16q^{86} + 12q^{87} - 12q^{88} - 4q^{89} + 32q^{93} + 8q^{94} - 24q^{95} - 2q^{96} - 12q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6762))\) 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 23
6762.2.a.a \(1\) \(53.995\) \(\Q\) None \(-1\) \(-1\) \(-3\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.b \(1\) \(53.995\) \(\Q\) None \(-1\) \(-1\) \(-3\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.c \(1\) \(53.995\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.d \(1\) \(53.995\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.e \(1\) \(53.995\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
6762.2.a.f \(1\) \(53.995\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
6762.2.a.g \(1\) \(53.995\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
6762.2.a.h \(1\) \(53.995\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
6762.2.a.i \(1\) \(53.995\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.j \(1\) \(53.995\) \(\Q\) None \(-1\) \(-1\) \(3\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.k \(1\) \(53.995\) \(\Q\) None \(-1\) \(1\) \(-3\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.l \(1\) \(53.995\) \(\Q\) None \(-1\) \(1\) \(-3\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.m \(1\) \(53.995\) \(\Q\) None \(-1\) \(1\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.n \(1\) \(53.995\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.o \(1\) \(53.995\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
6762.2.a.p \(1\) \(53.995\) \(\Q\) None \(-1\) \(1\) \(2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.q \(1\) \(53.995\) \(\Q\) None \(-1\) \(1\) \(2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.r \(1\) \(53.995\) \(\Q\) None \(-1\) \(1\) \(2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.s \(1\) \(53.995\) \(\Q\) None \(-1\) \(1\) \(2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.t \(1\) \(53.995\) \(\Q\) None \(-1\) \(1\) \(3\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.u \(1\) \(53.995\) \(\Q\) None \(-1\) \(1\) \(3\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.v \(1\) \(53.995\) \(\Q\) None \(-1\) \(1\) \(4\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.w \(1\) \(53.995\) \(\Q\) None \(1\) \(-1\) \(-4\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.x \(1\) \(53.995\) \(\Q\) None \(1\) \(-1\) \(-3\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.y \(1\) \(53.995\) \(\Q\) None \(1\) \(-1\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.z \(1\) \(53.995\) \(\Q\) None \(1\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
6762.2.a.ba \(1\) \(53.995\) \(\Q\) None \(1\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
6762.2.a.bb \(1\) \(53.995\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.bc \(1\) \(53.995\) \(\Q\) None \(1\) \(-1\) \(2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.bd \(1\) \(53.995\) \(\Q\) None \(1\) \(-1\) \(3\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.be \(1\) \(53.995\) \(\Q\) None \(1\) \(-1\) \(3\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.bf \(1\) \(53.995\) \(\Q\) None \(1\) \(1\) \(-3\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots\)
6762.2.a.bg \(1\) \(53.995\) \(\Q\) None \(1\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
6762.2.a.bh \(1\) \(53.995\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
6762.2.a.bi \(1\) \(53.995\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
6762.2.a.bj \(1\) \(53.995\) \(\Q\) None \(1\) \(1\) \(0\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
6762.2.a.bk \(1\) \(53.995\) \(\Q\) None \(1\) \(1\) \(0\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
6762.2.a.bl \(1\) \(53.995\) \(\Q\) None \(1\) \(1\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots\)
6762.2.a.bm \(1\) \(53.995\) \(\Q\) None \(1\) \(1\) \(3\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{8}+\cdots\)
6762.2.a.bn \(1\) \(53.995\) \(\Q\) None \(1\) \(1\) \(4\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+q^{8}+\cdots\)
6762.2.a.bo \(2\) \(53.995\) \(\Q(\sqrt{41}) \) None \(-2\) \(-2\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-\beta q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.bp \(2\) \(53.995\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.bq \(2\) \(53.995\) \(\Q(\sqrt{41}) \) None \(-2\) \(-2\) \(1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.br \(2\) \(53.995\) \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.bs \(2\) \(53.995\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(2\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
6762.2.a.bt \(2\) \(53.995\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(2\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
6762.2.a.bu \(2\) \(53.995\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}-q^{6}+\cdots\)
6762.2.a.bv \(2\) \(53.995\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}-q^{6}+\cdots\)
6762.2.a.bw \(2\) \(53.995\) \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.bx \(2\) \(53.995\) \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.by \(2\) \(53.995\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.bz \(2\) \(53.995\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-4\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.ca \(2\) \(53.995\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(2\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.cb \(2\) \(53.995\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
6762.2.a.cc \(2\) \(53.995\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
6762.2.a.cd \(2\) \(53.995\) \(\Q(\sqrt{33}) \) None \(2\) \(2\) \(3\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
6762.2.a.ce \(3\) \(53.995\) 3.3.3132.1 None \(-3\) \(-3\) \(3\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.cf \(3\) \(53.995\) 3.3.3132.1 None \(-3\) \(3\) \(-3\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.cg \(4\) \(53.995\) 4.4.138768.1 None \(-4\) \(-4\) \(2\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.ch \(4\) \(53.995\) 4.4.138768.1 None \(-4\) \(4\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.ci \(4\) \(53.995\) 4.4.2624.1 None \(4\) \(-4\) \(-8\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(-2-\beta _{1})q^{5}-q^{6}+\cdots\)
6762.2.a.cj \(4\) \(53.995\) 4.4.23252.1 None \(4\) \(-4\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-1+\beta _{3})q^{5}-q^{6}+\cdots\)
6762.2.a.ck \(4\) \(53.995\) 4.4.10304.1 None \(4\) \(-4\) \(2\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}-q^{6}+\cdots\)
6762.2.a.cl \(4\) \(53.995\) 4.4.473376.1 None \(4\) \(-4\) \(2\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots\)
6762.2.a.cm \(4\) \(53.995\) 4.4.42048.1 None \(4\) \(-4\) \(4\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(1-\beta _{2})q^{5}-q^{6}+\cdots\)
6762.2.a.cn \(4\) \(53.995\) 4.4.16448.2 None \(4\) \(-4\) \(6\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}-q^{6}+\cdots\)
6762.2.a.co \(4\) \(53.995\) 4.4.16448.2 None \(4\) \(4\) \(-6\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(-1-\beta _{1})q^{5}+q^{6}+\cdots\)
6762.2.a.cp \(4\) \(53.995\) 4.4.42048.1 None \(4\) \(4\) \(-4\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{2})q^{5}+q^{6}+\cdots\)
6762.2.a.cq \(4\) \(53.995\) 4.4.10304.1 None \(4\) \(4\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
6762.2.a.cr \(4\) \(53.995\) 4.4.473376.1 None \(4\) \(4\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots\)
6762.2.a.cs \(4\) \(53.995\) 4.4.23252.1 None \(4\) \(4\) \(3\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(1-\beta _{3})q^{5}+q^{6}+\cdots\)
6762.2.a.ct \(4\) \(53.995\) 4.4.2624.1 None \(4\) \(4\) \(8\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(2+\beta _{1})q^{5}+q^{6}+\cdots\)
6762.2.a.cu \(8\) \(53.995\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(-8\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-\beta _{7}q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.cv \(8\) \(53.995\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(8\) \(2\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+\beta _{7}q^{5}-q^{6}-q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6762))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6762)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(966))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1127))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2254))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3381))\)\(^{\oplus 2}\)