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Properties

Label 1610.2.bj
Level $1610$
Weight $2$
Character orbit 1610.bj
Rep. character $\chi_{1610}(43,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $1440$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1610 = 2 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1610.bj (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1610, [\chi])\).

Total New Old
Modular forms 5920 1440 4480
Cusp forms 5600 1440 4160
Eisenstein series 320 0 320

Trace form

\( 1440 q + 16 q^{3} + O(q^{10}) \) \( 1440 q + 16 q^{3} + 16 q^{12} - 32 q^{13} + 144 q^{16} + 72 q^{18} + 80 q^{23} - 32 q^{25} - 32 q^{27} - 32 q^{31} + 88 q^{33} - 144 q^{36} + 88 q^{37} + 64 q^{41} - 16 q^{46} + 176 q^{47} - 16 q^{48} - 16 q^{50} - 32 q^{52} + 88 q^{57} + 16 q^{62} + 352 q^{66} - 16 q^{70} + 688 q^{71} - 16 q^{72} + 64 q^{73} + 72 q^{75} - 64 q^{78} + 528 q^{81} - 16 q^{82} + 16 q^{85} - 48 q^{87} - 8 q^{92} - 80 q^{93} - 40 q^{95} - 264 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1610, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1610, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1610, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(805, [\chi])\)\(^{\oplus 2}\)