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Properties

Label 3600.2.ds
Level $3600$
Weight $2$
Character orbit 3600.ds
Rep. character $\chi_{3600}(241,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1424$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3600.ds (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3600, [\chi])\).

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

Trace form

\( 1424 q + 6 q^{3} - 4 q^{5} + 8 q^{7} - 6 q^{9} + O(q^{10}) \) \( 1424 q + 6 q^{3} - 4 q^{5} + 8 q^{7} - 6 q^{9} - 9 q^{11} - 3 q^{13} + 5 q^{15} - 12 q^{17} + 12 q^{19} + 3 q^{21} + 3 q^{23} - 4 q^{25} + 30 q^{27} - 3 q^{29} + 3 q^{31} - 12 q^{33} - 24 q^{35} - 12 q^{37} + 12 q^{39} - 3 q^{41} + 8 q^{43} - 13 q^{45} + 15 q^{47} - 672 q^{49} + 4 q^{51} - 12 q^{53} + 26 q^{55} + 12 q^{57} - 33 q^{59} - 3 q^{61} - 51 q^{63} - 22 q^{65} + 3 q^{67} - 12 q^{69} - 44 q^{71} - 12 q^{73} - 41 q^{75} + 39 q^{77} + 3 q^{79} + 42 q^{81} + 3 q^{83} + q^{85} + 40 q^{87} - 12 q^{89} - 30 q^{91} - 22 q^{93} + 17 q^{95} - 3 q^{97} + 34 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3600, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 2}\)