↑

Properties

Label 1510.2.be
Level $1510$
Weight $2$
Character orbit 1510.be
Rep. character $\chi_{1510}(3,\cdot)$
Character field $\Q(\zeta_{100})$
Dimension $3040$
Sturm bound $456$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1510 = 2 \cdot 5 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1510.be (of order \(100\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 755 \)
Character field: \(\Q(\zeta_{100})\)
Sturm bound: \(456\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1510, [\chi])\).

Total New Old
Modular forms 9280 3040 6240
Cusp forms 8960 3040 5920
Eisenstein series 320 0 320

Trace form

\( 3040 q + O(q^{10}) \) \( 3040 q - 80 q^{10} + 40 q^{11} - 80 q^{15} + 760 q^{16} + 80 q^{31} - 40 q^{41} + 20 q^{42} + 40 q^{43} - 100 q^{45} + 80 q^{50} + 100 q^{53} - 60 q^{55} + 40 q^{57} + 80 q^{58} + 240 q^{62} + 40 q^{63} + 160 q^{65} - 320 q^{67} - 20 q^{70} + 80 q^{71} - 80 q^{73} + 320 q^{81} - 240 q^{83} + 60 q^{90} - 160 q^{91} - 100 q^{95} - 140 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1510, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1510, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1510, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(755, [\chi])\)\(^{\oplus 2}\)