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Properties

Label 3312.2.dq
Level $3312$
Weight $2$
Character orbit 3312.dq
Rep. character $\chi_{3312}(59,\cdot)$
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.dq (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

\( 22880 q - 54 q^{2} - 36 q^{3} - 18 q^{4} - 54 q^{5} - 42 q^{6} - 36 q^{7} + O(q^{10}) \) \( 22880 q - 54 q^{2} - 36 q^{3} - 18 q^{4} - 54 q^{5} - 42 q^{6} - 36 q^{7} - 72 q^{10} - 54 q^{11} - 24 q^{12} - 18 q^{13} - 54 q^{14} - 18 q^{16} - 44 q^{18} - 72 q^{19} - 54 q^{20} - 48 q^{21} - 40 q^{22} - 120 q^{23} - 80 q^{24} - 24 q^{27} - 104 q^{28} - 54 q^{29} - 44 q^{30} - 54 q^{32} - 72 q^{33} - 26 q^{34} - 26 q^{36} - 72 q^{37} - 54 q^{38} - 48 q^{39} - 18 q^{40} - 100 q^{42} - 18 q^{43} - 100 q^{45} - 48 q^{46} - 128 q^{48} + 1060 q^{49} - 210 q^{50} - 60 q^{51} - 18 q^{52} - 36 q^{54} - 144 q^{55} - 138 q^{56} - 36 q^{58} - 18 q^{59} - 20 q^{60} - 18 q^{61} - 36 q^{64} - 108 q^{65} - 68 q^{66} - 18 q^{67} - 324 q^{68} - 34 q^{69} - 12 q^{70} - 84 q^{72} - 222 q^{74} - 44 q^{75} + 6 q^{76} - 54 q^{77} - 138 q^{78} - 72 q^{81} - 52 q^{82} - 54 q^{83} - 64 q^{84} - 38 q^{85} - 54 q^{86} - 72 q^{87} - 18 q^{88} - 160 q^{90} - 216 q^{91} - 174 q^{92} - 308 q^{93} + 54 q^{94} - 104 q^{96} - 36 q^{97} - 72 q^{99} + O(q^{100}) \)

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.