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Properties

Label 348.3
Level 348
Weight 3
Dimension 2878
Nonzero newspaces 12
Newform subspaces 14
Sturm bound 20160
Trace bound 7

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Defining parameters

Level: \( N \) = \( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 14 \)
Sturm bound: \(20160\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(348))\).

Total New Old
Modular forms 7000 2990 4010
Cusp forms 6440 2878 3562
Eisenstein series 560 112 448

Trace form

\( 2878 q + 4 q^{2} + 6 q^{3} - 20 q^{4} + 8 q^{5} - 26 q^{6} - 4 q^{7} - 32 q^{8} - 34 q^{9} + O(q^{10}) \) \( 2878 q + 4 q^{2} + 6 q^{3} - 20 q^{4} + 8 q^{5} - 26 q^{6} - 4 q^{7} - 32 q^{8} - 34 q^{9} - 36 q^{10} + 10 q^{12} - 20 q^{13} + 48 q^{14} + 4 q^{16} - 40 q^{17} - 26 q^{18} - 52 q^{19} - 16 q^{20} - 260 q^{21} - 76 q^{22} - 140 q^{23} - 14 q^{24} - 190 q^{25} + 8 q^{26} + 12 q^{27} - 96 q^{28} + 108 q^{29} - 4 q^{30} + 260 q^{31} + 64 q^{32} + 230 q^{33} + 12 q^{34} + 392 q^{35} - 38 q^{36} + 40 q^{37} - 144 q^{38} + 176 q^{39} + 36 q^{40} - 232 q^{41} + 34 q^{42} + 44 q^{43} + 460 q^{44} + 116 q^{45} + 1704 q^{46} + 560 q^{47} + 898 q^{48} + 926 q^{49} + 1288 q^{50} + 336 q^{51} + 1108 q^{52} + 800 q^{53} + 22 q^{54} + 448 q^{55} + 196 q^{56} + 300 q^{57} - 416 q^{58} - 112 q^{59} - 566 q^{60} - 756 q^{61} - 1028 q^{62} - 204 q^{63} - 2048 q^{64} - 992 q^{65} - 1070 q^{66} - 1364 q^{67} - 2076 q^{68} - 892 q^{69} - 3036 q^{70} - 784 q^{71} - 338 q^{72} - 900 q^{73} - 372 q^{74} + 920 q^{75} + 260 q^{76} - 192 q^{77} - 38 q^{78} + 284 q^{79} - 64 q^{80} + 334 q^{81} + 204 q^{82} - 44 q^{84} + 24 q^{85} + 336 q^{86} - 70 q^{87} - 56 q^{88} - 328 q^{89} + 10 q^{90} + 88 q^{91} - 384 q^{92} - 648 q^{93} - 508 q^{94} - 620 q^{96} + 2704 q^{97} - 2376 q^{98} - 14 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(348))\)

We only show spaces with odd 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
348.3.d \(\chi_{348}(233, \cdot)\) 348.3.d.a 4 1
348.3.d.b 14
348.3.e \(\chi_{348}(173, \cdot)\) 348.3.e.a 4 1
348.3.e.b 16
348.3.f \(\chi_{348}(175, \cdot)\) 348.3.f.a 56 1
348.3.g \(\chi_{348}(115, \cdot)\) 348.3.g.a 60 1
348.3.j \(\chi_{348}(133, \cdot)\) 348.3.j.a 20 2
348.3.k \(\chi_{348}(191, \cdot)\) 348.3.k.a 232 2
348.3.o \(\chi_{348}(67, \cdot)\) 348.3.o.a 360 6
348.3.p \(\chi_{348}(7, \cdot)\) 348.3.p.a 360 6
348.3.q \(\chi_{348}(5, \cdot)\) 348.3.q.a 120 6
348.3.r \(\chi_{348}(53, \cdot)\) 348.3.r.a 120 6
348.3.v \(\chi_{348}(11, \cdot)\) 348.3.v.a 1392 12
348.3.w \(\chi_{348}(37, \cdot)\) 348.3.w.a 120 12

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(348))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(348)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(348))\)\(^{\oplus 1}\)