↑

Properties

Label 3312.2.bc
Level $3312$
Weight $2$
Character orbit 3312.bc
Rep. character $\chi_{3312}(689,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $284$
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.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 1176 292 884
Cusp forms 1128 284 844
Eisenstein series 48 8 40

Trace form

\( 284 q + 4 q^{3} - 4 q^{9} + O(q^{10}) \) \( 284 q + 4 q^{3} - 4 q^{9} - 2 q^{13} + 3 q^{23} - 136 q^{25} + 22 q^{27} + 18 q^{29} + 2 q^{31} + 4 q^{39} - 6 q^{41} + 42 q^{47} + 128 q^{49} - 12 q^{55} - 12 q^{59} - 25 q^{69} - 8 q^{73} - 24 q^{75} + 42 q^{77} - 28 q^{81} - 12 q^{85} - 14 q^{87} - 26 q^{93} - 24 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3312, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(414, [\chi])\)\(^{\oplus 4}\)