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Properties

Label 2352.2.bp
Level $2352$
Weight $2$
Character orbit 2352.bp
Rep. character $\chi_{2352}(509,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1248$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.bp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 336 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2352, [\chi])\).

Total New Old
Modular forms 1856 1312 544
Cusp forms 1728 1248 480
Eisenstein series 128 64 64

Trace form

\( 1248 q + 6 q^{3} + 4 q^{4} + O(q^{10}) \) \( 1248 q + 6 q^{3} + 4 q^{4} + 12 q^{10} + 6 q^{12} - 32 q^{15} + 36 q^{16} + 28 q^{18} + 12 q^{19} - 8 q^{22} + 6 q^{24} - 42 q^{30} + 24 q^{31} + 12 q^{33} + 80 q^{36} + 4 q^{37} - 48 q^{40} - 32 q^{43} + 6 q^{45} + 36 q^{46} + 46 q^{51} + 48 q^{52} + 90 q^{54} + 20 q^{58} - 2 q^{60} + 12 q^{61} - 80 q^{64} + 66 q^{66} + 68 q^{67} + 74 q^{72} - 24 q^{75} + 52 q^{78} + 8 q^{79} + 4 q^{81} - 72 q^{82} - 72 q^{85} - 28 q^{88} - 22 q^{93} - 24 q^{94} - 96 q^{96} - 52 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

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