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Properties

Label 2352.2.bv
Level $2352$
Weight $2$
Character orbit 2352.bv
Rep. character $\chi_{2352}(275,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1248$
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.bv (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 336 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 1856 1312 544
Cusp forms 1728 1248 480
Eisenstein series 128 64 64

Trace form

\( 1248 q + 2 q^{3} + 4 q^{4} + 8 q^{6} + O(q^{10}) \) \( 1248 q + 2 q^{3} + 4 q^{4} + 8 q^{6} + 4 q^{10} + 2 q^{12} + 16 q^{13} + 36 q^{16} + 8 q^{18} + 4 q^{19} - 8 q^{22} + 22 q^{24} + 8 q^{27} + 46 q^{30} + 4 q^{33} - 80 q^{36} + 4 q^{37} + 4 q^{39} - 8 q^{40} - 32 q^{43} - 18 q^{45} - 28 q^{46} + 88 q^{48} - 42 q^{51} - 8 q^{52} - 14 q^{54} + 32 q^{55} + 52 q^{58} + 62 q^{60} + 4 q^{61} + 16 q^{64} + 30 q^{66} + 68 q^{67} + 20 q^{69} + 74 q^{72} + 24 q^{75} + 112 q^{76} + 68 q^{78} + 4 q^{81} + 32 q^{82} + 8 q^{85} + 4 q^{87} + 36 q^{88} - 28 q^{90} - 22 q^{93} - 72 q^{94} - 36 q^{96} + 32 q^{97} - 52 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)