↑

Properties

Label 3380.2.bg
Level $3380$
Weight $2$
Character orbit 3380.bg
Rep. character $\chi_{3380}(23,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1768$
Sturm bound $1092$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3380.bg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 260 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1092\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3380, [\chi])\).

Total New Old
Modular forms 2296 1928 368
Cusp forms 2072 1768 304
Eisenstein series 224 160 64

Trace form

\( 1768 q + 6 q^{2} + 12 q^{6} + O(q^{10}) \) \( 1768 q + 6 q^{2} + 12 q^{6} - 14 q^{10} + 28 q^{12} - 4 q^{16} + 14 q^{17} + 30 q^{20} + 20 q^{22} + 36 q^{25} + 6 q^{28} + 8 q^{30} + 36 q^{32} + 12 q^{33} + 52 q^{36} - 18 q^{37} + 16 q^{38} - 132 q^{40} + 24 q^{41} - 40 q^{42} + 102 q^{45} + 12 q^{46} - 32 q^{48} - 78 q^{50} - 84 q^{53} + 20 q^{56} - 66 q^{58} + 8 q^{61} + 44 q^{62} - 192 q^{66} - 52 q^{68} + 54 q^{72} + 12 q^{76} - 40 q^{77} - 24 q^{80} + 572 q^{81} + 18 q^{82} + 12 q^{85} - 22 q^{88} + 20 q^{90} - 148 q^{92} + 48 q^{93} + 12 q^{97} + 162 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3380, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 2}\)