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Properties

Label 1232.4.s
Level $1232$
Weight $4$
Character orbit 1232.s
Rep. character $\chi_{1232}(419,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $960$
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.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
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 960 200
Cusp forms 1144 960 184
Eisenstein series 16 0 16

Trace form

\( 960 q - 168 q^{8} + O(q^{10}) \) \( 960 q - 168 q^{8} + 104 q^{14} + 280 q^{18} - 380 q^{28} + 1160 q^{30} + 1960 q^{32} - 456 q^{35} + 440 q^{36} - 80 q^{42} - 1232 q^{44} - 1400 q^{46} - 2856 q^{50} - 2800 q^{51} + 2040 q^{56} - 1288 q^{58} + 1216 q^{60} + 3864 q^{64} + 3696 q^{67} - 5776 q^{70} + 448 q^{71} + 3976 q^{72} - 3640 q^{74} - 11632 q^{78} - 77760 q^{81} + 4484 q^{84} - 2312 q^{86} + 848 q^{91} + 5544 q^{92} + 7512 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{4}^{\mathrm{old}}(1232, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1232, [\chi]) \cong \)