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Properties

Label 3380.2.cx
Level $3380$
Weight $2$
Character orbit 3380.cx
Rep. character $\chi_{3380}(43,\cdot)$
Character field $\Q(\zeta_{156})$
Dimension $26016$
Sturm bound $1092$

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Defining parameters

Level: \( N \) \(=\) \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3380.cx (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

\( 26016 q - 46 q^{2} - 104 q^{5} - 92 q^{6} - 52 q^{8} + O(q^{10}) \) \( 26016 q - 46 q^{2} - 104 q^{5} - 92 q^{6} - 52 q^{8} - 50 q^{10} - 56 q^{12} - 98 q^{13} - 108 q^{16} - 90 q^{17} - 52 q^{18} - 22 q^{20} - 208 q^{21} - 22 q^{22} - 68 q^{25} - 72 q^{26} - 46 q^{28} - 60 q^{30} - 16 q^{32} - 92 q^{33} - 52 q^{36} - 122 q^{37} - 88 q^{38} - 104 q^{40} - 184 q^{41} + 428 q^{42} - 2 q^{45} - 92 q^{46} - 12 q^{48} - 130 q^{50} - 2 q^{52} - 66 q^{53} - 84 q^{56} - 260 q^{57} - 118 q^{58} - 52 q^{60} - 200 q^{61} - 8 q^{62} - 92 q^{65} + 216 q^{66} - 8 q^{68} + 2 q^{72} - 104 q^{73} - 300 q^{76} - 144 q^{77} + 48 q^{78} - 102 q^{80} - 1220 q^{81} - 2 q^{82} + 38 q^{85} - 104 q^{86} - 10 q^{88} - 32 q^{90} - 48 q^{92} - 56 q^{93} - 104 q^{96} - 92 q^{97} + 110 q^{98} + O(q^{100}) \)

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.