↑

Properties

Label 3510.2.bb
Level $3510$
Weight $2$
Character orbit 3510.bb
Rep. character $\chi_{3510}(361,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $112$
Sturm bound $1512$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3510 = 2 \cdot 3^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3510.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3510, [\chi])\).

Total New Old
Modular forms 1560 112 1448
Cusp forms 1464 112 1352
Eisenstein series 96 0 96

Trace form

\( 112 q + 56 q^{4} - 4 q^{13} - 56 q^{16} - 16 q^{17} - 12 q^{19} + 56 q^{25} - 8 q^{26} + 20 q^{29} + 12 q^{31} + 8 q^{35} + 12 q^{37} - 24 q^{38} + 8 q^{43} + 36 q^{47} - 128 q^{49} - 8 q^{52} - 32 q^{53}+ \cdots + 48 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(3510, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3510, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3510, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(702, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1170, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1755, [\chi])\)\(^{\oplus 2}\)