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Properties

Label 2352.4.bp
Level $2352$
Weight $4$
Character orbit 2352.bp
Rep. character $\chi_{2352}(509,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $3808$
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.bp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 336 \)
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 3872 1568
Cusp forms 5312 3808 1504
Eisenstein series 128 64 64

Trace form

\( 3808 q + 6 q^{3} + 4 q^{4} + O(q^{10}) \) \( 3808 q + 6 q^{3} + 4 q^{4} + 12 q^{10} + 6 q^{12} - 32 q^{15} - 476 q^{16} + 136 q^{18} + 12 q^{19} - 536 q^{22} + 6 q^{24} + 1146 q^{30} + 24 q^{31} + 12 q^{33} - 640 q^{36} + 4 q^{37} + 2352 q^{40} - 32 q^{43} + 6 q^{45} + 132 q^{46} - 482 q^{51} + 2496 q^{52} - 4446 q^{54} + 2548 q^{58} - 3290 q^{60} + 12 q^{61} + 2992 q^{64} + 3306 q^{66} - 3260 q^{67} - 2950 q^{72} - 744 q^{75} - 5900 q^{78} + 8 q^{79} + 4 q^{81} - 5304 q^{82} - 1032 q^{85} - 6428 q^{88} - 214 q^{93} - 7008 q^{94} + 9696 q^{96} - 2932 q^{99} + O(q^{100}) \)

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

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