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Properties

Label 3600.2.ep
Level $3600$
Weight $2$
Character orbit 3600.ep
Rep. character $\chi_{3600}(109,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2384$
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.ep (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 400 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 5824 2416 3408
Cusp forms 5696 2384 3312
Eisenstein series 128 32 96

Trace form

\( 2384 q + 10 q^{2} - 6 q^{4} + 8 q^{5} - 20 q^{8} + O(q^{10}) \) \( 2384 q + 10 q^{2} - 6 q^{4} + 8 q^{5} - 20 q^{8} - 2 q^{10} + 6 q^{11} - 10 q^{13} + 18 q^{14} - 6 q^{16} + 20 q^{17} - 6 q^{19} - 6 q^{20} - 10 q^{22} - 4 q^{26} - 50 q^{28} + 6 q^{29} - 36 q^{31} + 18 q^{34} + 60 q^{35} - 10 q^{37} - 60 q^{38} - 12 q^{40} + 48 q^{44} + 2 q^{46} + 20 q^{47} + 2256 q^{49} + 14 q^{50} + 80 q^{52} + 10 q^{53} + 48 q^{56} - 10 q^{58} + 6 q^{59} - 6 q^{61} + 10 q^{62} - 24 q^{64} - 16 q^{65} - 70 q^{67} - 28 q^{70} + 60 q^{74} - 4 q^{76} + 80 q^{77} - 52 q^{79} + 74 q^{80} + 10 q^{83} - 18 q^{85} - 34 q^{86} + 100 q^{88} - 48 q^{91} + 100 q^{92} + 34 q^{94} - 8 q^{95} - 20 q^{97} + 100 q^{98} + O(q^{100}) \)

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

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