Properties

Label 1200.4.cw
Level $1200$
Weight $4$
Character orbit 1200.cw
Rep. character $\chi_{1200}(17,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1424$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1200.cw (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1200, [\chi])\).

Total New Old
Modular forms 5856 1456 4400
Cusp forms 5664 1424 4240
Eisenstein series 192 32 160

Trace form

\( 1424 q + 8 q^{3} + 16 q^{7} - 10 q^{9} + O(q^{10}) \) \( 1424 q + 8 q^{3} + 16 q^{7} - 10 q^{9} - 16 q^{13} - 4 q^{15} + 20 q^{19} - 6 q^{21} - 16 q^{25} - 436 q^{27} + 12 q^{31} - 62 q^{33} - 544 q^{37} + 10 q^{39} - 416 q^{43} + 242 q^{45} + 16 q^{51} - 420 q^{55} + 786 q^{57} - 12 q^{61} - 998 q^{63} - 56 q^{67} - 10 q^{69} - 1000 q^{73} + 528 q^{75} + 20 q^{79} - 6 q^{81} - 7120 q^{85} - 690 q^{87} + 12 q^{91} + 46 q^{93} - 2992 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1200, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)