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Properties

Label 2352.3.x
Level $2352$
Weight $3$
Character orbit 2352.x
Rep. character $\chi_{2352}(883,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $656$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2352.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2352, [\chi])\).

Total New Old
Modular forms 1824 656 1168
Cusp forms 1760 656 1104
Eisenstein series 64 0 64

Trace form

\( 656 q - 12 q^{4} + 12 q^{8} + O(q^{10}) \) \( 656 q - 12 q^{4} + 12 q^{8} + 16 q^{10} - 32 q^{11} - 24 q^{12} + 24 q^{16} - 12 q^{18} - 32 q^{19} - 80 q^{20} + 80 q^{22} + 128 q^{23} + 36 q^{24} - 100 q^{26} - 32 q^{29} + 72 q^{30} + 160 q^{32} - 64 q^{34} + 12 q^{36} + 96 q^{37} - 112 q^{38} + 312 q^{40} - 32 q^{43} - 368 q^{44} - 224 q^{46} + 144 q^{48} - 204 q^{50} - 96 q^{51} + 160 q^{53} - 36 q^{54} - 256 q^{55} - 144 q^{58} + 128 q^{59} + 72 q^{60} - 32 q^{61} + 228 q^{62} + 408 q^{64} - 32 q^{65} - 72 q^{66} - 320 q^{67} + 72 q^{68} + 96 q^{69} - 512 q^{71} - 60 q^{72} + 172 q^{74} + 192 q^{75} + 192 q^{76} - 396 q^{78} - 472 q^{80} - 5904 q^{81} + 480 q^{82} - 160 q^{83} + 160 q^{85} + 88 q^{86} - 176 q^{88} - 24 q^{90} - 808 q^{92} + 1056 q^{94} + 120 q^{96} - 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)