↑

Properties

Label 1610.2.bv
Level $1610$
Weight $2$
Character orbit 1610.bv
Rep. character $\chi_{1610}(3,\cdot)$
Character field $\Q(\zeta_{132})$
Dimension $3840$
Sturm bound $576$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1610 = 2 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1610.bv (of order \(132\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 805 \)
Character field: \(\Q(\zeta_{132})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 11840 3840 8000
Cusp forms 11200 3840 7360
Eisenstein series 640 0 640

Trace form

\( 3840 q + 24 q^{5} - 8 q^{7} + O(q^{10}) \) \( 3840 q + 24 q^{5} - 8 q^{7} + 8 q^{11} - 192 q^{16} - 72 q^{18} + 24 q^{21} + 32 q^{22} + 92 q^{23} - 24 q^{25} - 24 q^{26} + 72 q^{28} - 16 q^{30} - 24 q^{31} + 8 q^{35} + 400 q^{36} - 72 q^{37} - 48 q^{38} + 16 q^{43} + 8 q^{46} - 24 q^{47} + 32 q^{51} - 16 q^{53} + 52 q^{56} + 176 q^{57} - 16 q^{60} - 72 q^{61} + 152 q^{63} - 40 q^{65} - 32 q^{67} + 16 q^{70} - 16 q^{71} + 16 q^{72} + 72 q^{73} - 80 q^{77} + 24 q^{80} - 208 q^{81} + 96 q^{82} - 200 q^{85} + 36 q^{86} + 144 q^{87} + 16 q^{88} - 8 q^{92} + 8 q^{93} + 4 q^{95} - 24 q^{96} - 24 q^{98} + O(q^{100}) \)

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

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