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Properties

Label 1232.4.co
Level $1232$
Weight $4$
Character orbit 1232.co
Rep. character $\chi_{1232}(13,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $4576$
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.co (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1232 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 4640 4640 0
Cusp forms 4576 4576 0
Eisenstein series 64 64 0

Trace form

\( 4576 q - 20 q^{2} - 32 q^{4} - 20 q^{8} + O(q^{10}) \) \( 4576 q - 20 q^{2} - 32 q^{4} - 20 q^{8} - 36 q^{11} + 130 q^{14} - 24 q^{15} - 312 q^{16} + 430 q^{18} + 2118 q^{22} - 10 q^{28} - 20 q^{29} - 20 q^{30} - 10 q^{35} - 524 q^{36} - 36 q^{37} - 1210 q^{42} - 1306 q^{44} + 140 q^{46} - 12 q^{49} - 20 q^{50} - 20 q^{51} + 1116 q^{53} + 3356 q^{56} + 2208 q^{58} + 5156 q^{60} - 20 q^{63} + 8584 q^{64} + 2008 q^{67} + 3292 q^{70} - 7670 q^{72} - 20 q^{74} + 678 q^{77} + 6800 q^{78} - 40 q^{79} + 87456 q^{81} - 12440 q^{84} - 20 q^{85} + 4390 q^{86} - 1718 q^{88} + 3174 q^{91} + 5710 q^{92} - 228 q^{93} - 40 q^{95} - 6640 q^{99} + O(q^{100}) \)

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.