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Properties

Label 1232.4.y
Level $1232$
Weight $4$
Character orbit 1232.y
Rep. character $\chi_{1232}(309,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $720$
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.y (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
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 720 440
Cusp forms 1144 720 424
Eisenstein series 16 0 16

Trace form

\( 720 q - 120 q^{6} + O(q^{10}) \) \( 720 q - 120 q^{6} - 240 q^{10} + 312 q^{12} - 480 q^{15} + 528 q^{16} - 96 q^{19} - 616 q^{20} - 912 q^{24} + 528 q^{27} + 2224 q^{30} + 1392 q^{34} - 3328 q^{36} - 2408 q^{38} + 192 q^{46} + 4888 q^{48} - 35280 q^{49} + 4264 q^{50} - 2976 q^{51} - 1728 q^{54} + 2376 q^{58} + 4080 q^{59} - 2440 q^{60} + 3648 q^{61} - 984 q^{62} - 1080 q^{64} - 1952 q^{65} + 2064 q^{68} + 2112 q^{69} + 504 q^{70} - 4624 q^{72} - 3640 q^{74} - 6608 q^{75} - 1664 q^{76} - 4992 q^{78} - 11328 q^{79} + 3160 q^{80} - 58320 q^{81} + 5728 q^{82} + 960 q^{85} + 7928 q^{86} + 8216 q^{90} + 1392 q^{92} - 8544 q^{93} + 8096 q^{94} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1232, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)