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Properties

Label 3234.2.i
Level $3234$
Weight $2$
Character orbit 3234.i
Rep. character $\chi_{3234}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $136$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1408 136 1272
Cusp forms 1280 136 1144
Eisenstein series 128 0 128

Trace form

\( 136 q - 68 q^{4} - 68 q^{9} + O(q^{10}) \) \( 136 q - 68 q^{4} - 68 q^{9} - 68 q^{16} - 8 q^{19} + 32 q^{23} - 44 q^{25} - 32 q^{29} + 4 q^{33} - 24 q^{34} + 136 q^{36} - 44 q^{37} - 16 q^{38} - 48 q^{39} - 64 q^{41} + 16 q^{43} + 16 q^{46} - 8 q^{47} + 128 q^{50} + 16 q^{51} - 24 q^{53} + 80 q^{57} - 36 q^{58} - 16 q^{59} - 8 q^{61} + 136 q^{64} - 16 q^{65} + 8 q^{66} - 40 q^{67} - 24 q^{69} - 32 q^{71} - 16 q^{73} - 16 q^{74} - 8 q^{75} + 16 q^{76} + 16 q^{79} - 68 q^{81} + 16 q^{82} - 32 q^{83} + 208 q^{85} + 16 q^{86} - 24 q^{87} - 40 q^{89} - 64 q^{92} - 40 q^{93} - 16 q^{94} + 64 q^{95} - 120 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1078, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)