Properties

Label 1232.2.dn
Level $1232$
Weight $2$
Character orbit 1232.dn
Rep. character $\chi_{1232}(37,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3008$
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.dn (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1232 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 3136 3136 0
Cusp forms 3008 3008 0
Eisenstein series 128 128 0

Trace form

\( 3008 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{5} - 24 q^{6} - 24 q^{8} + O(q^{10}) \) \( 3008 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{5} - 24 q^{6} - 24 q^{8} - 16 q^{10} - 4 q^{11} - 16 q^{12} - 24 q^{13} + 12 q^{14} - 48 q^{15} - 26 q^{16} - 12 q^{17} + 40 q^{18} - 6 q^{19} - 40 q^{20} - 20 q^{21} - 124 q^{22} - 6 q^{24} - 6 q^{26} + 28 q^{28} - 56 q^{29} + 2 q^{30} - 12 q^{31} - 16 q^{32} - 16 q^{33} - 80 q^{34} + 8 q^{35} + 8 q^{36} - 30 q^{37} - 6 q^{38} - 6 q^{40} - 80 q^{42} - 48 q^{43} + 12 q^{44} + 36 q^{45} - 30 q^{46} - 12 q^{47} - 104 q^{48} - 24 q^{49} - 64 q^{50} - 30 q^{51} + 18 q^{52} + 18 q^{53} - 184 q^{54} - 8 q^{56} + 14 q^{58} + 10 q^{59} + 70 q^{60} - 6 q^{61} + 48 q^{62} + 32 q^{63} + 64 q^{64} - 32 q^{65} + 8 q^{66} - 56 q^{67} - 38 q^{68} - 60 q^{69} - 70 q^{70} - 68 q^{72} + 10 q^{74} + 38 q^{75} - 64 q^{76} - 2 q^{77} + 96 q^{78} - 12 q^{79} - 138 q^{80} - 324 q^{81} - 14 q^{82} - 24 q^{83} - 270 q^{84} - 64 q^{85} - 104 q^{86} + 24 q^{88} - 36 q^{90} + 20 q^{91} + 116 q^{92} - 30 q^{93} - 142 q^{94} - 12 q^{95} - 6 q^{96} - 48 q^{97} - 216 q^{98} + 152 q^{99} + O(q^{100}) \)

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

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