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Properties

Label 3234.2.bl
Level $3234$
Weight $2$
Character orbit 3234.bl
Rep. character $\chi_{3234}(557,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1280$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3234.bl (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3234, [\chi])\).

Total New Old
Modular forms 5632 1280 4352
Cusp forms 5120 1280 3840
Eisenstein series 512 0 512

Trace form

\( 1280 q + 160 q^{4} - 24 q^{9} + O(q^{10}) \) \( 1280 q + 160 q^{4} - 24 q^{9} + 48 q^{15} + 160 q^{16} - 12 q^{22} - 180 q^{25} + 36 q^{27} + 6 q^{31} - 24 q^{33} + 32 q^{34} - 32 q^{36} - 12 q^{37} - 40 q^{39} - 10 q^{40} - 56 q^{45} - 40 q^{51} + 84 q^{55} + 80 q^{57} + 38 q^{58} + 16 q^{60} - 80 q^{61} - 320 q^{64} + 48 q^{66} - 32 q^{67} + 136 q^{69} + 20 q^{72} - 20 q^{73} + 28 q^{75} + 96 q^{78} + 76 q^{81} + 16 q^{82} + 240 q^{85} + 6 q^{88} + 160 q^{90} - 38 q^{93} - 80 q^{94} + 32 q^{97} + 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3234, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3234, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)