↑

Properties

Label 3380.2.cu
Level $3380$
Weight $2$
Character orbit 3380.cu
Rep. character $\chi_{3380}(3,\cdot)$
Character field $\Q(\zeta_{156})$
Dimension $26016$
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.cu (of order \(156\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3380 \)
Character field: \(\Q(\zeta_{156})\)
Sturm bound: \(1092\)

Dimensions

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

Total New Old
Modular forms 26400 26400 0
Cusp forms 26016 26016 0
Eisenstein series 384 384 0

Trace form

\( 26016 q - 50 q^{2} - 88 q^{5} - 100 q^{6} - 44 q^{8} + O(q^{10}) \) \( 26016 q - 50 q^{2} - 88 q^{5} - 100 q^{6} - 44 q^{8} - 50 q^{10} - 56 q^{12} - 94 q^{13} - 92 q^{16} - 110 q^{17} - 24 q^{18} - 78 q^{20} - 176 q^{21} - 6 q^{22} - 68 q^{25} - 88 q^{26} - 66 q^{28} - 40 q^{30} - 40 q^{32} - 76 q^{33} - 84 q^{36} - 90 q^{37} - 64 q^{40} - 216 q^{41} - 516 q^{42} - 110 q^{45} - 100 q^{46} - 64 q^{48} - 58 q^{50} - 42 q^{52} - 66 q^{53} - 84 q^{56} + 76 q^{57} - 18 q^{58} - 140 q^{60} - 200 q^{61} - 52 q^{62} - 60 q^{65} - 392 q^{66} - 8 q^{68} - 212 q^{70} - 78 q^{72} - 140 q^{73} + 44 q^{76} - 32 q^{77} + 68 q^{78} + 22 q^{80} - 1220 q^{81} - 18 q^{82} - 210 q^{85} - 80 q^{86} - 42 q^{88} + 16 q^{90} + 136 q^{92} - 112 q^{93} - 264 q^{96} - 120 q^{97} - 122 q^{98} + O(q^{100}) \)

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.