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Properties

Label 3600.2.du
Level $3600$
Weight $2$
Character orbit 3600.du
Rep. character $\chi_{3600}(181,\cdot)$
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.du (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

\( 2384 q + 6 q^{2} - 6 q^{4} + 8 q^{5} + 24 q^{8} + O(q^{10}) \) \( 2384 q + 6 q^{2} - 6 q^{4} + 8 q^{5} + 24 q^{8} - 14 q^{10} + 6 q^{11} - 6 q^{13} - 6 q^{14} - 6 q^{16} + 12 q^{17} - 6 q^{19} + 22 q^{20} - 22 q^{22} + 36 q^{26} + 18 q^{28} + 6 q^{29} + 12 q^{31} - 4 q^{32} + 34 q^{34} - 20 q^{35} - 6 q^{37} + 20 q^{38} - 44 q^{40} + 16 q^{43} + 48 q^{44} - 14 q^{46} + 12 q^{47} - 2320 q^{49} - 18 q^{50} + 64 q^{52} + 6 q^{53} - 36 q^{56} - 38 q^{58} + 6 q^{59} - 6 q^{61} - 38 q^{62} - 24 q^{64} + 48 q^{65} + 30 q^{67} + 28 q^{68} + 36 q^{70} + 60 q^{74} - 28 q^{76} - 36 q^{77} - 52 q^{79} + 42 q^{80} - 24 q^{82} - 34 q^{83} + 2 q^{85} + 46 q^{86} - 104 q^{88} + 36 q^{91} - 108 q^{92} + 10 q^{94} - 8 q^{95} - 12 q^{97} - 56 q^{98} + O(q^{100}) \)

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

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