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Properties

Label 1332.2.ci
Level $1332$
Weight $2$
Character orbit 1332.ci
Rep. character $\chi_{1332}(199,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $372$
Sturm bound $456$

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Defining parameters

Level: \( N \) \(=\) \( 1332 = 2^{2} \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1332.ci (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 148 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(456\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1332, [\chi])\).

Total New Old
Modular forms 944 388 556
Cusp forms 880 372 508
Eisenstein series 64 16 48

Trace form

\( 372 q + 2 q^{2} + 12 q^{5} + 8 q^{8} + O(q^{10}) \) \( 372 q + 2 q^{2} + 12 q^{5} + 8 q^{8} - 8 q^{10} - 2 q^{13} - 4 q^{16} - 2 q^{17} + 26 q^{20} - 12 q^{22} - 42 q^{25} + 8 q^{26} - 6 q^{28} + 26 q^{29} - 8 q^{32} - 18 q^{34} - 24 q^{37} - 40 q^{38} - 6 q^{40} + 12 q^{41} + 52 q^{44} + 6 q^{46} + 134 q^{49} + 48 q^{52} + 4 q^{53} + 46 q^{56} - 72 q^{58} - 14 q^{61} + 36 q^{62} + 66 q^{65} - 48 q^{68} + 18 q^{70} + 132 q^{74} - 36 q^{76} + 48 q^{77} + 20 q^{80} + 36 q^{82} - 2 q^{86} + 36 q^{88} + 42 q^{89} + 58 q^{92} + 76 q^{94} + 26 q^{97} + 38 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1332, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1332, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1332, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(444, [\chi])\)\(^{\oplus 2}\)