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Properties

Label 2352.2.br
Level $2352$
Weight $2$
Character orbit 2352.br
Rep. character $\chi_{2352}(373,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $640$
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.br (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
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 640 1216
Cusp forms 1728 640 1088
Eisenstein series 128 0 128

Trace form

\( 640 q - 8 q^{4} - 24 q^{8} + O(q^{10}) \) \( 640 q - 8 q^{4} - 24 q^{8} + 12 q^{10} - 16 q^{11} + 8 q^{16} + 8 q^{18} + 32 q^{20} - 40 q^{22} + 64 q^{29} + 48 q^{31} - 32 q^{34} - 32 q^{37} + 40 q^{38} + 52 q^{40} - 32 q^{43} + 24 q^{44} + 20 q^{46} - 32 q^{48} + 136 q^{50} + 24 q^{52} + 32 q^{53} + 4 q^{58} - 32 q^{59} + 48 q^{60} + 144 q^{62} + 184 q^{64} - 24 q^{66} + 40 q^{67} + 20 q^{68} - 8 q^{72} + 12 q^{74} - 24 q^{76} + 120 q^{78} - 100 q^{80} + 320 q^{81} - 20 q^{82} + 120 q^{86} - 52 q^{88} - 152 q^{92} - 60 q^{94} + 48 q^{95} - 20 q^{96} + 32 q^{99} + O(q^{100}) \)

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

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