↑

Properties

Label 3600.3.eg
Level $3600$
Weight $3$
Character orbit 3600.eg
Rep. character $\chi_{3600}(37,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $4784$
Sturm bound $2160$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3600.eg (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

\( 4784 q + 8 q^{2} - 10 q^{4} + 8 q^{5} + 14 q^{8} + O(q^{10}) \) \( 4784 q + 8 q^{2} - 10 q^{4} + 8 q^{5} + 14 q^{8} - 16 q^{10} + 6 q^{11} - 10 q^{13} + 10 q^{14} + 194 q^{16} + 16 q^{17} - 10 q^{19} - 34 q^{20} + 160 q^{22} + 16 q^{26} - 14 q^{28} + 10 q^{29} - 12 q^{31} + 18 q^{32} - 10 q^{34} - 240 q^{35} - 10 q^{37} - 46 q^{38} + 464 q^{40} + 112 q^{43} - 340 q^{44} - 6 q^{46} + 16 q^{47} - 494 q^{50} + 840 q^{52} + 6 q^{53} + 6 q^{56} + 398 q^{58} + 10 q^{59} - 6 q^{61} + 166 q^{62} - 460 q^{64} + 16 q^{65} - 438 q^{67} - 326 q^{68} - 310 q^{70} - 48 q^{73} + 16 q^{74} - 16 q^{76} - 288 q^{77} - 20 q^{79} - 880 q^{80} + 286 q^{82} + 10 q^{83} - 58 q^{85} - 454 q^{86} + 70 q^{88} - 496 q^{91} + 126 q^{92} - 10 q^{94} - 368 q^{95} - 16 q^{97} + 548 q^{98} + O(q^{100}) \)

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

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