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Properties

Label 3600.3.dw
Level $3600$
Weight $3$
Character orbit 3600.dw
Rep. character $\chi_{3600}(19,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $4784$
Sturm bound $2160$

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Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3600.dw (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 400 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(2160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3600, [\chi])\).

Total New Old
Modular forms 11584 4816 6768
Cusp forms 11456 4784 6672
Eisenstein series 128 32 96

Trace form

\( 4784 q + 10 q^{2} - 6 q^{4} + 8 q^{5} - 20 q^{8} + O(q^{10}) \) \( 4784 q + 10 q^{2} - 6 q^{4} + 8 q^{5} - 20 q^{8} + 10 q^{10} + 6 q^{11} - 10 q^{13} - 18 q^{14} - 6 q^{16} + 20 q^{17} - 6 q^{19} + 50 q^{20} - 10 q^{22} + 20 q^{23} + 116 q^{26} + 150 q^{28} + 6 q^{29} - 182 q^{34} - 144 q^{35} - 10 q^{37} + 640 q^{38} - 460 q^{40} + 216 q^{44} - 22 q^{46} - 32848 q^{49} + 46 q^{50} - 280 q^{52} + 10 q^{53} - 272 q^{55} - 288 q^{56} - 10 q^{58} + 6 q^{59} - 6 q^{61} + 10 q^{62} + 264 q^{64} - 48 q^{65} + 710 q^{67} + 396 q^{70} + 12 q^{71} - 204 q^{74} + 44 q^{76} - 480 q^{77} + 42 q^{80} + 10 q^{83} - 58 q^{85} - 594 q^{86} + 980 q^{88} + 288 q^{91} + 1180 q^{92} + 410 q^{94} - 20 q^{97} - 440 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(3600, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)