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Properties

Label 2352.4.br
Level $2352$
Weight $4$
Character orbit 2352.br
Rep. character $\chi_{2352}(373,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1920$
Sturm bound $1792$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2352.br (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2352, [\chi])\).

Total New Old
Modular forms 5440 1920 3520
Cusp forms 5312 1920 3392
Eisenstein series 128 0 128

Trace form

\( 1920 q - 40 q^{4} + 168 q^{8} + O(q^{10}) \) \( 1920 q - 40 q^{4} + 168 q^{8} - 12 q^{10} - 80 q^{11} - 120 q^{16} - 72 q^{18} + 160 q^{20} - 440 q^{22} - 1600 q^{29} - 1488 q^{31} + 288 q^{34} + 32 q^{37} + 440 q^{38} - 492 q^{40} - 3232 q^{43} + 2232 q^{44} + 700 q^{46} - 1056 q^{48} + 56 q^{50} - 2376 q^{52} + 1504 q^{53} - 3268 q^{58} + 1376 q^{59} - 2448 q^{60} - 1872 q^{62} + 2744 q^{64} + 1368 q^{66} + 1032 q^{67} + 2020 q^{68} - 1224 q^{72} + 4788 q^{74} + 1224 q^{76} + 3816 q^{78} + 220 q^{80} + 77760 q^{81} - 1740 q^{82} - 5592 q^{86} - 1300 q^{88} + 15176 q^{92} - 180 q^{94} + 7728 q^{95} - 2580 q^{96} + 1440 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

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