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Properties

Label 3312.2.cu
Level $3312$
Weight $2$
Character orbit 3312.cu
Rep. character $\chi_{3312}(19,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $4760$
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.cu (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 368 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 11680 4840 6840
Cusp forms 11360 4760 6600
Eisenstein series 320 80 240

Trace form

\( 4760 q + 18 q^{2} - 22 q^{4} + 22 q^{5} - 44 q^{7} + 18 q^{8} + O(q^{10}) \) \( 4760 q + 18 q^{2} - 22 q^{4} + 22 q^{5} - 44 q^{7} + 18 q^{8} - 22 q^{10} + 22 q^{11} - 18 q^{13} + 22 q^{14} - 6 q^{16} + 44 q^{17} - 22 q^{19} + 22 q^{20} + 32 q^{23} + 38 q^{26} - 22 q^{28} + 34 q^{29} + 38 q^{32} + 22 q^{34} + 38 q^{35} - 22 q^{37} + 132 q^{38} - 22 q^{40} - 22 q^{43} + 22 q^{44} - 158 q^{46} + 416 q^{49} - 28 q^{50} - 14 q^{52} + 22 q^{53} - 36 q^{55} + 22 q^{56} - 50 q^{58} + 30 q^{59} - 22 q^{61} + 44 q^{62} - 64 q^{64} + 44 q^{65} - 22 q^{67} - 32 q^{70} + 36 q^{71} + 22 q^{74} - 22 q^{76} + 118 q^{77} + 22 q^{80} - 8 q^{82} + 22 q^{83} - 70 q^{85} + 22 q^{86} - 22 q^{88} + 74 q^{92} - 110 q^{94} - 44 q^{97} + 6 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3312, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3312, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(368, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1104, [\chi])\)\(^{\oplus 2}\)