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Properties

Label 354.4.e
Level $354$
Weight $4$
Character orbit 354.e
Rep. character $\chi_{354}(7,\cdot)$
Character field $\Q(\zeta_{29})$
Dimension $840$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 354.e (of order \(29\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q(\zeta_{29})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(354, [\chi])\).

Total New Old
Modular forms 5152 840 4312
Cusp forms 4928 840 4088
Eisenstein series 224 0 224

Trace form

\( 840 q - 120 q^{4} - 12 q^{6} - 12 q^{7} - 270 q^{9} + O(q^{10}) \) \( 840 q - 120 q^{4} - 12 q^{6} - 12 q^{7} - 270 q^{9} - 16 q^{10} - 136 q^{11} - 84 q^{13} - 64 q^{14} + 84 q^{15} - 480 q^{16} - 72 q^{17} + 56 q^{19} + 280 q^{22} - 128 q^{23} - 48 q^{24} - 1090 q^{25} + 304 q^{26} - 48 q^{28} - 72 q^{29} - 120 q^{30} + 108 q^{31} - 120 q^{33} - 656 q^{34} + 88 q^{35} - 1080 q^{36} + 36 q^{37} - 128 q^{38} - 24 q^{39} - 64 q^{40} + 272 q^{41} + 192 q^{42} + 12 q^{43} - 544 q^{44} - 10760 q^{46} - 8976 q^{47} - 8810 q^{49} - 3024 q^{50} - 792 q^{51} + 1520 q^{52} + 6512 q^{53} - 108 q^{54} + 14280 q^{55} - 256 q^{56} - 768 q^{57} + 6712 q^{58} + 14116 q^{59} + 336 q^{60} + 9532 q^{61} + 4952 q^{62} - 108 q^{63} - 1920 q^{64} + 3264 q^{65} + 624 q^{66} - 4684 q^{67} - 4000 q^{68} - 240 q^{69} - 17696 q^{70} - 26184 q^{71} - 19732 q^{73} - 21784 q^{74} - 960 q^{75} + 224 q^{76} - 1112 q^{77} - 144 q^{78} + 2788 q^{79} - 2430 q^{81} - 480 q^{82} + 2272 q^{83} - 240 q^{85} - 256 q^{86} - 972 q^{87} + 1120 q^{88} + 3848 q^{89} - 144 q^{90} - 176 q^{91} - 512 q^{92} - 564 q^{93} + 2288 q^{94} + 4528 q^{95} - 192 q^{96} + 28 q^{97} + 512 q^{98} - 1224 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(354, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(354, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(354, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(118, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)