↑

Properties

Label 3380.2.r
Level $3380$
Weight $2$
Character orbit 3380.r
Rep. character $\chi_{3380}(437,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $154$
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.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(i)\)
Sturm bound: \(1092\)

Dimensions

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

Total New Old
Modular forms 1176 154 1022
Cusp forms 1008 154 854
Eisenstein series 168 0 168

Trace form

\( 154 q - 2 q^{5} + O(q^{10}) \) \( 154 q - 2 q^{5} + 12 q^{15} + 2 q^{17} + 12 q^{19} + 12 q^{21} - 8 q^{23} - 18 q^{25} + 24 q^{27} - 24 q^{35} + 4 q^{37} - 2 q^{41} - 16 q^{43} + 12 q^{45} - 32 q^{47} + 146 q^{49} + 22 q^{53} + 28 q^{55} - 16 q^{59} - 8 q^{61} + 64 q^{69} + 12 q^{71} - 28 q^{75} + 56 q^{77} - 178 q^{81} + 56 q^{83} + 70 q^{85} + 8 q^{87} + 18 q^{89} + 52 q^{93} - 40 q^{95} - 20 q^{99} + O(q^{100}) \)

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

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