↑

Properties

Label 3312.2.q
Level $3312$
Weight $2$
Character orbit 3312.q
Rep. character $\chi_{3312}(1105,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $264$
Sturm bound $1152$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3312 = 2^{4} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3312.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3312, [\chi])\).

Total New Old
Modular forms 1176 264 912
Cusp forms 1128 264 864
Eisenstein series 48 0 48

Trace form

\( 264 q + 4 q^{9} + O(q^{10}) \) \( 264 q + 4 q^{9} + 8 q^{17} + 6 q^{23} - 132 q^{25} + 6 q^{27} - 12 q^{31} + 12 q^{33} + 48 q^{35} + 54 q^{39} + 4 q^{41} - 12 q^{43} + 20 q^{47} - 132 q^{49} - 4 q^{51} - 12 q^{57} - 42 q^{59} - 76 q^{63} - 104 q^{71} + 24 q^{73} - 92 q^{75} - 4 q^{81} - 20 q^{83} + 16 q^{87} - 16 q^{89} + 24 q^{91} - 12 q^{93} + 68 q^{95} - 12 q^{97} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3312, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3312, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3312, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(414, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(828, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1656, [\chi])\)\(^{\oplus 2}\)