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Properties

Label 3234.2.bj
Level $3234$
Weight $2$
Character orbit 3234.bj
Rep. character $\chi_{3234}(19,\cdot)$
Character field $\Q(\zeta_{30})$
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.bj (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
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 640 4992
Cusp forms 5120 640 4480
Eisenstein series 512 0 512

Trace form

\( 640 q - 80 q^{4} + 24 q^{5} - 80 q^{9} + O(q^{10}) \) \( 640 q - 80 q^{4} + 24 q^{5} - 80 q^{9} - 8 q^{11} + 12 q^{15} + 80 q^{16} - 60 q^{17} + 12 q^{22} - 8 q^{23} - 108 q^{25} + 24 q^{26} + 40 q^{29} - 18 q^{31} + 6 q^{33} - 160 q^{36} + 36 q^{37} - 24 q^{38} - 30 q^{40} - 12 q^{44} + 24 q^{45} - 48 q^{47} - 40 q^{51} - 10 q^{58} - 4 q^{60} + 60 q^{61} + 160 q^{64} - 64 q^{67} + 60 q^{68} + 144 q^{71} + 180 q^{73} + 40 q^{74} - 24 q^{75} + 60 q^{79} + 36 q^{80} + 80 q^{81} + 96 q^{82} + 280 q^{85} + 36 q^{86} + 26 q^{88} + 48 q^{89} - 16 q^{92} + 40 q^{93} + 20 q^{95} - 16 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1078, [\chi])\)\(^{\oplus 2}\)