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Properties

Label 1610.2.m
Level $1610$
Weight $2$
Character orbit 1610.m
Rep. character $\chi_{1610}(783,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $176$
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.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 592 176 416
Cusp forms 560 176 384
Eisenstein series 32 0 32

Trace form

\( 176 q + 8 q^{7} + O(q^{10}) \) \( 176 q + 8 q^{7} - 16 q^{11} + 32 q^{15} - 176 q^{16} - 32 q^{21} + 16 q^{22} - 8 q^{28} - 48 q^{30} + 24 q^{35} - 192 q^{36} - 48 q^{37} - 64 q^{50} + 48 q^{53} + 16 q^{57} + 32 q^{58} - 16 q^{63} + 16 q^{65} + 32 q^{67} - 8 q^{70} + 16 q^{71} + 24 q^{77} + 32 q^{78} - 208 q^{81} + 32 q^{85} + 16 q^{86} - 16 q^{88} + 64 q^{91} + 64 q^{93} - 96 q^{95} - 32 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1610, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)