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Properties

Label 1232.4.x
Level $1232$
Weight $4$
Character orbit 1232.x
Rep. character $\chi_{1232}(461,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $1144$
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.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1232 \)
Character field: \(\Q(i)\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 1160 1160 0
Cusp forms 1144 1144 0
Eisenstein series 16 16 0

Trace form

\( 1144 q + 12 q^{4} + O(q^{10}) \) \( 1144 q + 12 q^{4} + 16 q^{11} - 140 q^{14} - 16 q^{15} + 292 q^{16} + 382 q^{22} + 504 q^{36} - 24 q^{37} + 1200 q^{42} + 1286 q^{44} - 8 q^{49} + 744 q^{53} - 876 q^{56} - 2228 q^{58} + 4624 q^{60} + 6516 q^{64} - 2048 q^{67} + 128 q^{70} - 688 q^{77} - 7200 q^{78} - 87496 q^{81} + 8340 q^{86} + 1698 q^{88} + 5816 q^{91} + 5600 q^{92} + 208 q^{93} + 2120 q^{99} + O(q^{100}) \)

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.