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Properties

Label 931.4
Level 931
Weight 4
Dimension 100176
Nonzero newspaces 32
Sturm bound 282240
Trace bound 10

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Defining parameters

Level: \( N \) = \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(282240\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(931))\).

Total New Old
Modular forms 106920 101824 5096
Cusp forms 104760 100176 4584
Eisenstein series 2160 1648 512

Trace form

\( 100176 q - 249 q^{2} - 273 q^{3} - 249 q^{4} - 201 q^{5} - 117 q^{6} - 240 q^{7} - 549 q^{8} - 417 q^{9} + O(q^{10}) \) \( 100176 q - 249 q^{2} - 273 q^{3} - 249 q^{4} - 201 q^{5} - 117 q^{6} - 240 q^{7} - 549 q^{8} - 417 q^{9} - 357 q^{10} - 249 q^{11} - 357 q^{12} - 381 q^{13} - 240 q^{14} - 45 q^{15} + 423 q^{16} + 207 q^{17} + 156 q^{18} - 198 q^{19} - 612 q^{20} - 744 q^{21} - 303 q^{22} + 573 q^{23} - 117 q^{24} + 159 q^{25} - 921 q^{26} - 1422 q^{27} + 96 q^{28} - 1023 q^{29} - 1698 q^{30} - 867 q^{31} - 1206 q^{32} + 885 q^{33} + 336 q^{34} - 408 q^{35} + 6489 q^{36} + 3264 q^{37} + 4701 q^{38} + 5658 q^{39} + 9324 q^{40} + 4413 q^{41} - 534 q^{42} - 2535 q^{43} - 10074 q^{44} - 12963 q^{45} - 13260 q^{46} - 6777 q^{47} - 21810 q^{48} - 8052 q^{49} - 12426 q^{50} - 7272 q^{51} - 9957 q^{52} - 2865 q^{53} - 2436 q^{54} - 345 q^{55} + 180 q^{56} + 4884 q^{57} + 8460 q^{58} + 10881 q^{59} + 24150 q^{60} + 7293 q^{61} + 9912 q^{62} + 9420 q^{63} + 7611 q^{64} - 663 q^{65} - 3549 q^{66} - 1839 q^{67} - 5676 q^{68} - 9849 q^{69} - 1038 q^{70} - 9123 q^{71} + 3456 q^{72} + 6348 q^{73} + 4179 q^{74} + 7134 q^{75} + 7248 q^{76} - 144 q^{77} + 5745 q^{78} + 4599 q^{79} + 26289 q^{80} + 34680 q^{81} + 28488 q^{82} + 21933 q^{83} + 38400 q^{84} + 10839 q^{85} + 9120 q^{86} + 2019 q^{87} - 5583 q^{88} - 4251 q^{89} - 33204 q^{90} - 10698 q^{91} - 18900 q^{92} - 43563 q^{93} - 40716 q^{94} - 25458 q^{95} - 71850 q^{96} - 25719 q^{97} - 55260 q^{98} - 33600 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(931))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
931.4.a \(\chi_{931}(1, \cdot)\) 931.4.a.a 1 1
931.4.a.b 1
931.4.a.c 3
931.4.a.d 6
931.4.a.e 6
931.4.a.f 7
931.4.a.g 8
931.4.a.h 14
931.4.a.i 14
931.4.a.j 16
931.4.a.k 16
931.4.a.l 20
931.4.a.m 20
931.4.a.n 26
931.4.a.o 26
931.4.c \(\chi_{931}(930, \cdot)\) n/a 196 1
931.4.e \(\chi_{931}(197, \cdot)\) n/a 400 2
931.4.f \(\chi_{931}(324, \cdot)\) n/a 360 2
931.4.g \(\chi_{931}(30, \cdot)\) n/a 392 2
931.4.h \(\chi_{931}(410, \cdot)\) n/a 392 2
931.4.i \(\chi_{931}(411, \cdot)\) n/a 392 2
931.4.o \(\chi_{931}(227, \cdot)\) n/a 392 2
931.4.p \(\chi_{931}(293, \cdot)\) n/a 392 2
931.4.s \(\chi_{931}(31, \cdot)\) n/a 392 2
931.4.u \(\chi_{931}(134, \cdot)\) n/a 1512 6
931.4.v \(\chi_{931}(177, \cdot)\) n/a 1176 6
931.4.w \(\chi_{931}(99, \cdot)\) n/a 1200 6
931.4.x \(\chi_{931}(226, \cdot)\) n/a 1176 6
931.4.z \(\chi_{931}(132, \cdot)\) n/a 1668 6
931.4.be \(\chi_{931}(48, \cdot)\) n/a 1176 6
931.4.bf \(\chi_{931}(325, \cdot)\) n/a 1176 6
931.4.bj \(\chi_{931}(117, \cdot)\) n/a 1176 6
931.4.bk \(\chi_{931}(11, \cdot)\) n/a 3336 12
931.4.bl \(\chi_{931}(102, \cdot)\) n/a 3336 12
931.4.bm \(\chi_{931}(39, \cdot)\) n/a 3024 12
931.4.bn \(\chi_{931}(64, \cdot)\) n/a 3336 12
931.4.bp \(\chi_{931}(103, \cdot)\) n/a 3336 12
931.4.bs \(\chi_{931}(27, \cdot)\) n/a 3336 12
931.4.bt \(\chi_{931}(75, \cdot)\) n/a 3336 12
931.4.bz \(\chi_{931}(12, \cdot)\) n/a 3336 12
931.4.ca \(\chi_{931}(4, \cdot)\) n/a 10008 36
931.4.cb \(\chi_{931}(9, \cdot)\) n/a 10008 36
931.4.cc \(\chi_{931}(36, \cdot)\) n/a 10008 36
931.4.cd \(\chi_{931}(10, \cdot)\) n/a 10008 36
931.4.ch \(\chi_{931}(13, \cdot)\) n/a 10008 36
931.4.ci \(\chi_{931}(3, \cdot)\) n/a 10008 36

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(931))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(931)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 2}\)