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Properties

Label 1200.2.cw
Level $1200$
Weight $2$
Character orbit 1200.cw
Rep. character $\chi_{1200}(17,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $464$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1200.cw (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1200, [\chi])\).

Total New Old
Modular forms 2016 496 1520
Cusp forms 1824 464 1360
Eisenstein series 192 32 160

Trace form

\( 464 q + 8 q^{3} + 16 q^{7} - 10 q^{9} + O(q^{10}) \) \( 464 q + 8 q^{3} + 16 q^{7} - 10 q^{9} - 16 q^{13} - 4 q^{15} + 20 q^{19} - 6 q^{21} - 16 q^{25} - 4 q^{27} + 12 q^{31} - 14 q^{33} + 10 q^{39} + 32 q^{43} + 2 q^{45} + 16 q^{51} + 60 q^{55} - 30 q^{57} - 12 q^{61} + 58 q^{63} + 40 q^{67} - 10 q^{69} - 24 q^{73} + 48 q^{75} + 20 q^{79} - 6 q^{81} - 80 q^{85} + 30 q^{87} + 12 q^{91} - 2 q^{93} + 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

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