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Properties

Label 1224.4.q
Level $1224$
Weight $4$
Character orbit 1224.q
Rep. character $\chi_{1224}(409,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $288$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1224.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1224, [\chi])\).

Total New Old
Modular forms 1312 288 1024
Cusp forms 1280 288 992
Eisenstein series 32 0 32

Trace form

\( 288 q + 20 q^{5} - 28 q^{9} + O(q^{10}) \) \( 288 q + 20 q^{5} - 28 q^{9} - 132 q^{11} - 164 q^{15} - 136 q^{17} - 416 q^{21} + 104 q^{23} - 3600 q^{25} - 888 q^{27} + 264 q^{29} - 180 q^{31} + 80 q^{33} - 488 q^{39} + 1068 q^{41} + 252 q^{43} - 892 q^{45} - 1164 q^{47} - 7452 q^{49} - 1136 q^{53} - 1224 q^{55} - 1384 q^{57} + 36 q^{61} - 120 q^{63} + 2684 q^{65} + 5800 q^{69} + 1120 q^{71} + 3592 q^{75} + 1564 q^{77} - 252 q^{79} - 3080 q^{81} - 940 q^{83} - 208 q^{87} - 1272 q^{89} - 3960 q^{91} - 4344 q^{93} - 3664 q^{95} + 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1224, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1224, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1224, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(306, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(612, [\chi])\)\(^{\oplus 2}\)