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Properties

Label 2352.3.bw
Level $2352$
Weight $3$
Character orbit 2352.bw
Rep. character $\chi_{2352}(325,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1280$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2352.bw (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2352, [\chi])\).

Total New Old
Modular forms 3648 1280 2368
Cusp forms 3520 1280 2240
Eisenstein series 128 0 128

Trace form

\( 1280 q + 24 q^{4} + 24 q^{8} + O(q^{10}) \) \( 1280 q + 24 q^{4} + 24 q^{8} - 108 q^{10} - 64 q^{11} + 8 q^{16} - 24 q^{18} - 120 q^{22} + 128 q^{29} + 192 q^{37} - 60 q^{40} + 384 q^{43} - 280 q^{44} - 180 q^{46} - 248 q^{50} - 720 q^{52} - 320 q^{53} + 364 q^{58} - 384 q^{59} - 144 q^{60} + 600 q^{64} + 216 q^{66} + 352 q^{67} + 780 q^{68} - 120 q^{72} + 396 q^{74} + 504 q^{78} + 612 q^{80} + 5760 q^{81} - 780 q^{82} + 376 q^{86} + 532 q^{88} + 2280 q^{92} + 612 q^{94} - 768 q^{95} + 900 q^{96} - 384 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)