Properties

Label 342.4
Level 342
Weight 4
Dimension 2551
Nonzero newspaces 16
Sturm bound 25920
Trace bound 4

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Defining parameters

Level: \( N \) = \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(25920\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(342))\).

Total New Old
Modular forms 10008 2551 7457
Cusp forms 9432 2551 6881
Eisenstein series 576 0 576

Trace form

\( 2551 q - 8 q^{2} - 6 q^{3} + 16 q^{4} - 24 q^{5} + 36 q^{6} + 8 q^{7} + 16 q^{8} + 210 q^{9} + O(q^{10}) \) \( 2551 q - 8 q^{2} - 6 q^{3} + 16 q^{4} - 24 q^{5} + 36 q^{6} + 8 q^{7} + 16 q^{8} + 210 q^{9} + 24 q^{10} - 54 q^{11} - 48 q^{12} + 260 q^{13} - 100 q^{14} - 180 q^{15} + 64 q^{16} - 384 q^{17} - 312 q^{18} - 986 q^{19} - 384 q^{20} + 72 q^{21} - 78 q^{22} + 900 q^{23} + 48 q^{24} + 1480 q^{25} + 1316 q^{26} + 752 q^{28} + 1386 q^{29} + 576 q^{30} + 278 q^{31} - 128 q^{32} - 1530 q^{33} - 684 q^{34} - 3972 q^{35} - 1032 q^{36} - 1558 q^{37} - 362 q^{38} + 1164 q^{39} + 96 q^{40} + 48 q^{41} + 1632 q^{42} - 2674 q^{43} - 1980 q^{44} - 6804 q^{45} - 6168 q^{46} - 3426 q^{47} + 3054 q^{49} + 2152 q^{50} + 4986 q^{51} + 536 q^{52} + 8844 q^{53} + 3492 q^{54} + 14328 q^{55} + 5504 q^{56} + 9093 q^{57} + 5448 q^{58} + 12834 q^{59} + 5040 q^{60} + 7946 q^{61} + 7892 q^{62} + 5604 q^{63} - 896 q^{64} - 4062 q^{65} - 5472 q^{66} - 11854 q^{67} - 3372 q^{68} - 13788 q^{69} - 14424 q^{70} - 23730 q^{71} - 3264 q^{72} - 5671 q^{73} - 2728 q^{74} - 6462 q^{75} + 340 q^{76} + 702 q^{77} - 264 q^{78} + 6614 q^{79} + 1344 q^{80} - 630 q^{81} + 8232 q^{82} + 1002 q^{83} - 1488 q^{84} + 1008 q^{85} - 412 q^{86} + 6408 q^{87} + 336 q^{88} + 6258 q^{89} + 864 q^{90} - 5744 q^{91} + 288 q^{92} + 5268 q^{93} - 8376 q^{94} - 27672 q^{95} - 768 q^{96} - 26290 q^{97} - 10764 q^{98} - 14526 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(342))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
342.4.a \(\chi_{342}(1, \cdot)\) 342.4.a.a 1 1
342.4.a.b 1
342.4.a.c 1
342.4.a.d 1
342.4.a.e 1
342.4.a.f 2
342.4.a.g 2
342.4.a.h 2
342.4.a.i 2
342.4.a.j 2
342.4.a.k 2
342.4.a.l 3
342.4.a.m 3
342.4.b \(\chi_{342}(341, \cdot)\) 342.4.b.a 10 1
342.4.b.b 10
342.4.e \(\chi_{342}(115, \cdot)\) n/a 108 2
342.4.f \(\chi_{342}(7, \cdot)\) n/a 120 2
342.4.g \(\chi_{342}(163, \cdot)\) 342.4.g.a 2 2
342.4.g.b 2
342.4.g.c 2
342.4.g.d 2
342.4.g.e 4
342.4.g.f 6
342.4.g.g 6
342.4.g.h 6
342.4.g.i 10
342.4.g.j 10
342.4.h \(\chi_{342}(121, \cdot)\) n/a 120 2
342.4.j \(\chi_{342}(65, \cdot)\) n/a 120 2
342.4.n \(\chi_{342}(293, \cdot)\) n/a 120 2
342.4.p \(\chi_{342}(113, \cdot)\) n/a 120 2
342.4.s \(\chi_{342}(107, \cdot)\) 342.4.s.a 20 2
342.4.s.b 20
342.4.u \(\chi_{342}(55, \cdot)\) n/a 150 6
342.4.v \(\chi_{342}(25, \cdot)\) n/a 360 6
342.4.w \(\chi_{342}(43, \cdot)\) n/a 360 6
342.4.x \(\chi_{342}(29, \cdot)\) n/a 360 6
342.4.bb \(\chi_{342}(53, \cdot)\) n/a 120 6
342.4.bf \(\chi_{342}(155, \cdot)\) n/a 360 6

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(342))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(342)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 2}\)