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Properties

Label 1232.4.dm
Level $1232$
Weight $4$
Character orbit 1232.dm
Rep. character $\chi_{1232}(61,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $9152$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1232.dm (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1232 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1232, [\chi])\).

Total New Old
Modular forms 9280 9280 0
Cusp forms 9152 9152 0
Eisenstein series 128 128 0

Trace form

\( 9152 q - 10 q^{2} - 18 q^{3} + 14 q^{4} - 18 q^{5} - 40 q^{8} + O(q^{10}) \) \( 9152 q - 10 q^{2} - 18 q^{3} + 14 q^{4} - 18 q^{5} - 40 q^{8} + 12 q^{11} - 48 q^{12} + 164 q^{14} - 48 q^{15} + 294 q^{16} - 60 q^{17} - 460 q^{18} - 30 q^{19} - 1812 q^{22} - 30 q^{24} - 18 q^{26} - 20 q^{28} - 40 q^{29} - 10 q^{30} - 36 q^{31} - 48 q^{33} - 20 q^{35} + 488 q^{36} + 18 q^{37} - 18 q^{38} - 30 q^{40} - 1400 q^{42} - 1028 q^{44} + 276 q^{45} - 170 q^{46} - 36 q^{47} - 24 q^{49} - 40 q^{50} - 10 q^{51} - 30 q^{52} - 1134 q^{53} + 712 q^{56} - 2226 q^{58} + 2046 q^{59} + 4414 q^{60} - 30 q^{61} - 40 q^{63} - 10048 q^{64} + 4080 q^{66} - 2056 q^{67} - 30 q^{68} + 410 q^{70} + 7640 q^{72} - 10 q^{74} + 1482 q^{75} - 702 q^{77} - 7760 q^{78} - 20 q^{79} - 18 q^{80} - 87492 q^{81} - 114 q^{82} + 12410 q^{84} - 40 q^{85} - 9280 q^{86} + 2156 q^{88} - 7308 q^{91} + 9116 q^{92} + 210 q^{93} - 30 q^{94} - 20 q^{95} - 30 q^{96} - 4208 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1232, [\chi])\) into newform subspaces

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