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Properties

Label 3312.2.cq
Level $3312$
Weight $2$
Character orbit 3312.cq
Rep. character $\chi_{3312}(35,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $3840$
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.cq (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1104 \)
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 3840 7840
Cusp forms 11360 3840 7520
Eisenstein series 320 0 320

Trace form

\( 3840 q + O(q^{10}) \) \( 3840 q + 16 q^{10} + 32 q^{16} - 32 q^{19} - 136 q^{34} - 144 q^{40} + 312 q^{46} - 384 q^{49} - 64 q^{52} - 136 q^{58} + 64 q^{61} + 32 q^{67} - 48 q^{76} - 80 q^{82} + 64 q^{85} + 16 q^{88} - 192 q^{94} + O(q^{100}) \)

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

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