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Properties

Label 3312.2.dm
Level $3312$
Weight $2$
Character orbit 3312.dm
Rep. character $\chi_{3312}(43,\cdot)$
Character field $\Q(\zeta_{132})$
Dimension $22880$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 3312 = 2^{4} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3312.dm (of order \(132\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3312 \)
Character field: \(\Q(\zeta_{132})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 23200 23200 0
Cusp forms 22880 22880 0
Eisenstein series 320 320 0

Trace form

\( 22880 q - 18 q^{2} - 36 q^{3} - 18 q^{4} - 22 q^{5} - 42 q^{6} - 44 q^{7} - 72 q^{8} + O(q^{10}) \) \( 22880 q - 18 q^{2} - 36 q^{3} - 18 q^{4} - 22 q^{5} - 42 q^{6} - 44 q^{7} - 72 q^{8} - 88 q^{10} - 22 q^{11} - 24 q^{12} - 18 q^{13} - 22 q^{14} - 18 q^{16} - 176 q^{17} - 28 q^{18} - 88 q^{19} - 22 q^{20} - 44 q^{21} - 40 q^{23} - 80 q^{24} - 72 q^{26} - 24 q^{27} - 88 q^{28} - 18 q^{29} - 44 q^{30} - 18 q^{32} - 88 q^{33} - 22 q^{34} - 32 q^{35} - 26 q^{36} - 88 q^{37} - 22 q^{38} - 96 q^{39} - 22 q^{40} - 44 q^{42} - 22 q^{43} - 88 q^{44} - 64 q^{46} + 56 q^{48} - 1132 q^{49} - 54 q^{50} - 44 q^{51} - 18 q^{52} - 88 q^{53} - 36 q^{54} - 144 q^{55} - 22 q^{56} - 30 q^{59} - 44 q^{60} - 22 q^{61} - 44 q^{62} - 36 q^{64} - 44 q^{65} - 44 q^{66} - 22 q^{67} - 46 q^{69} - 68 q^{70} - 144 q^{71} + 12 q^{72} - 22 q^{74} - 44 q^{75} - 22 q^{76} + 38 q^{77} - 154 q^{78} - 88 q^{80} - 72 q^{81} - 92 q^{82} - 22 q^{83} - 44 q^{84} - 38 q^{85} - 22 q^{86} - 72 q^{87} - 22 q^{88} - 44 q^{90} - 74 q^{92} + 172 q^{93} - 90 q^{94} + 32 q^{96} - 44 q^{97} - 168 q^{98} - 44 q^{99} + O(q^{100}) \)

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.