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Properties

Label 2352.4.bt
Level $2352$
Weight $4$
Character orbit 2352.bt
Rep. character $\chi_{2352}(19,\cdot)$
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.bt (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

\( 1920 q - 40 q^{4} - 168 q^{8} + O(q^{10}) \) \( 1920 q - 40 q^{4} - 168 q^{8} + 36 q^{10} + 80 q^{11} - 120 q^{16} + 72 q^{18} + 1448 q^{22} - 1312 q^{23} + 1600 q^{29} - 32 q^{37} + 2340 q^{40} + 3232 q^{43} + 232 q^{44} + 700 q^{46} - 5656 q^{50} - 2160 q^{52} + 1504 q^{53} - 1252 q^{58} - 4128 q^{59} - 2448 q^{60} + 8792 q^{64} - 4104 q^{66} - 2664 q^{67} + 6060 q^{68} + 896 q^{71} + 1224 q^{72} + 476 q^{74} - 3816 q^{78} + 7524 q^{80} + 77760 q^{81} + 5220 q^{82} + 5592 q^{86} + 1300 q^{88} - 12696 q^{92} - 7020 q^{94} - 7740 q^{96} + 1440 q^{99} + O(q^{100}) \)

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

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