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Properties

Label 1200.3.bt
Level $1200$
Weight $3$
Character orbit 1200.bt
Rep. character $\chi_{1200}(31,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $240$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1200.bt (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1200, [\chi])\).

Total New Old
Modular forms 1968 240 1728
Cusp forms 1872 240 1632
Eisenstein series 96 0 96

Trace form

\( 240 q - 12 q^{5} + 180 q^{9} + O(q^{10}) \) \( 240 q - 12 q^{5} + 180 q^{9} + 72 q^{13} + 24 q^{17} - 12 q^{25} - 120 q^{29} - 144 q^{33} + 36 q^{37} + 120 q^{41} + 36 q^{45} - 1440 q^{49} - 252 q^{53} - 120 q^{61} - 132 q^{65} - 408 q^{73} - 96 q^{77} - 540 q^{81} - 348 q^{85} - 180 q^{89} - 1152 q^{93} + 144 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)