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Properties

Label 3234.2.bo
Level $3234$
Weight $2$
Character orbit 3234.bo
Rep. character $\chi_{3234}(509,\cdot)$
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.bo (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

\( 1280 q - 160 q^{4} + 24 q^{9} + O(q^{10}) \) \( 1280 q - 160 q^{4} + 24 q^{9} - 12 q^{10} - 48 q^{15} + 160 q^{16} + 8 q^{18} + 20 q^{22} + 132 q^{25} - 18 q^{31} + 132 q^{33} - 32 q^{36} - 12 q^{37} + 20 q^{39} + 18 q^{40} - 64 q^{43} + 48 q^{45} - 16 q^{46} + 4 q^{51} + 88 q^{57} - 46 q^{58} + 16 q^{60} + 320 q^{64} + 120 q^{66} + 32 q^{67} + 12 q^{72} + 96 q^{73} + 204 q^{75} + 96 q^{78} + 52 q^{79} + 68 q^{81} - 24 q^{82} - 368 q^{85} + 228 q^{87} + 10 q^{88} - 22 q^{93} + 144 q^{94} - 48 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)