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Properties

Label 3234.2.t
Level $3234$
Weight $2$
Character orbit 3234.t
Rep. character $\chi_{3234}(587,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $640$
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.t (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 2816 640 2176
Cusp forms 2560 640 1920
Eisenstein series 256 0 256

Trace form

\( 640 q + 160 q^{4} - 24 q^{9} + O(q^{10}) \) \( 640 q + 160 q^{4} - 24 q^{9} - 24 q^{15} - 160 q^{16} + 16 q^{18} + 4 q^{22} - 144 q^{25} - 16 q^{36} + 24 q^{37} - 80 q^{39} + 64 q^{43} + 16 q^{46} + 32 q^{51} - 88 q^{57} - 92 q^{58} - 16 q^{60} + 160 q^{64} + 64 q^{67} + 24 q^{72} + 96 q^{78} - 184 q^{79} + 112 q^{81} - 40 q^{85} - 4 q^{88} + 100 q^{93} + 216 q^{99} + O(q^{100}) \)

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

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