Properties

Label 2352.2.w
Level $2352$
Weight $2$
Character orbit 2352.w
Rep. character $\chi_{2352}(589,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $328$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2352, [\chi])\).

Total New Old
Modular forms 928 328 600
Cusp forms 864 328 536
Eisenstein series 64 0 64

Trace form

\( 328 q + 4 q^{4} + 12 q^{8} + O(q^{10}) \) \( 328 q + 4 q^{4} + 12 q^{8} + 16 q^{10} + 8 q^{11} + 8 q^{12} - 8 q^{15} - 8 q^{16} - 4 q^{18} - 8 q^{19} - 16 q^{20} + 16 q^{22} + 4 q^{24} + 20 q^{26} + 16 q^{29} - 8 q^{30} - 24 q^{31} + 32 q^{34} - 4 q^{36} + 16 q^{37} - 48 q^{38} + 24 q^{40} - 24 q^{43} - 16 q^{44} + 32 q^{46} + 16 q^{48} - 4 q^{50} + 8 q^{51} + 32 q^{52} - 16 q^{53} + 4 q^{54} + 16 q^{58} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 60 q^{62} - 8 q^{64} - 16 q^{65} - 24 q^{66} + 16 q^{67} + 72 q^{68} + 16 q^{69} + 4 q^{72} - 92 q^{74} + 16 q^{75} + 32 q^{76} + 12 q^{78} - 24 q^{79} + 72 q^{80} - 328 q^{81} - 40 q^{83} - 16 q^{85} - 88 q^{86} - 48 q^{88} - 8 q^{90} - 200 q^{92} + 32 q^{94} + 48 q^{95} - 40 q^{96} + 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)