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Properties

Label 1232.2.ch
Level $1232$
Weight $2$
Character orbit 1232.ch
Rep. character $\chi_{1232}(219,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $752$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1232.ch (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1232 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1232, [\chi])\).

Total New Old
Modular forms 784 784 0
Cusp forms 752 752 0
Eisenstein series 32 32 0

Trace form

\( 752 q - 4 q^{3} - 8 q^{4} - 4 q^{5} + O(q^{10}) \) \( 752 q - 4 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{11} - 4 q^{12} - 32 q^{14} + 16 q^{16} - 32 q^{20} + 20 q^{22} + 8 q^{23} - 4 q^{26} - 40 q^{27} - 4 q^{33} - 32 q^{34} - 48 q^{36} + 12 q^{37} - 4 q^{38} + 60 q^{42} + 18 q^{44} - 32 q^{45} - 96 q^{48} - 16 q^{49} - 20 q^{53} - 16 q^{55} + 28 q^{56} + 16 q^{58} - 20 q^{59} - 20 q^{60} - 56 q^{64} - 34 q^{66} - 44 q^{67} + 8 q^{69} - 52 q^{70} + 32 q^{71} - 8 q^{75} - 18 q^{77} - 32 q^{78} - 92 q^{80} + 304 q^{81} - 12 q^{82} - 72 q^{86} - 14 q^{88} + 16 q^{91} + 144 q^{92} - 28 q^{93} - 32 q^{97} - 72 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1232, [\chi])\) into newform subspaces

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