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Properties

Label 3600.3.ec
Level $3600$
Weight $3$
Character orbit 3600.ec
Rep. character $\chi_{3600}(397,\cdot)$
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.ec (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

\( 4784 q + 8 q^{2} - 10 q^{4} + 8 q^{5} + 14 q^{8} + O(q^{10}) \) \( 4784 q + 8 q^{2} - 10 q^{4} + 8 q^{5} + 14 q^{8} + 6 q^{11} - 6 q^{13} + 10 q^{14} - 206 q^{16} + 16 q^{17} - 10 q^{19} + 50 q^{20} - 64 q^{22} + 16 q^{26} + 62 q^{28} + 10 q^{29} - 12 q^{31} + 138 q^{32} - 10 q^{34} + 160 q^{35} - 6 q^{37} - 162 q^{38} + 280 q^{40} - 340 q^{44} - 6 q^{46} + 16 q^{47} + 290 q^{50} - 216 q^{52} + 10 q^{53} + 6 q^{56} - 62 q^{58} + 10 q^{59} - 6 q^{61} + 86 q^{62} - 460 q^{64} + 16 q^{65} + 710 q^{67} + 98 q^{68} - 42 q^{70} + 48 q^{73} - 16 q^{74} - 16 q^{76} + 500 q^{77} - 20 q^{79} + 396 q^{80} - 718 q^{82} - 154 q^{83} + 42 q^{85} + 466 q^{86} + 342 q^{88} + 484 q^{91} + 66 q^{92} - 10 q^{94} - 368 q^{95} - 16 q^{97} - 80 q^{98} + O(q^{100}) \)

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

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