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Properties

Label 2352.3.t
Level $2352$
Weight $3$
Character orbit 2352.t
Rep. character $\chi_{2352}(197,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $1292$
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.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1824 1332 492
Cusp forms 1760 1292 468
Eisenstein series 64 40 24

Trace form

\( 1292 q + 2 q^{3} + 4 q^{4} + 8 q^{6} + O(q^{10}) \) \( 1292 q + 2 q^{3} + 4 q^{4} + 8 q^{6} - 16 q^{10} - 28 q^{12} + 4 q^{13} - 20 q^{15} - 40 q^{16} + 12 q^{18} - 28 q^{19} + 48 q^{22} + 88 q^{24} - 46 q^{27} + 112 q^{30} + 8 q^{31} + 4 q^{33} - 48 q^{34} - 76 q^{36} + 4 q^{37} - 88 q^{40} - 84 q^{43} + 52 q^{45} - 256 q^{46} - 164 q^{48} + 12 q^{51} - 48 q^{52} + 128 q^{54} + 208 q^{58} + 212 q^{60} - 28 q^{61} - 296 q^{64} - 144 q^{66} - 124 q^{67} + 20 q^{69} - 108 q^{72} + 46 q^{75} + 304 q^{76} + 320 q^{78} + 264 q^{79} + 4 q^{81} + 256 q^{82} - 280 q^{85} - 184 q^{88} + 328 q^{90} - 136 q^{93} + 384 q^{94} + 56 q^{96} + 8 q^{97} + 24 q^{99} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)