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Properties

Label 3600.3.bb
Level $3600$
Weight $3$
Character orbit 3600.bb
Rep. character $\chi_{3600}(757,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $716$
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.bb (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Sturm bound: \(2160\)

Dimensions

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

Total New Old
Modular forms 2928 724 2204
Cusp forms 2832 716 2116
Eisenstein series 96 8 88

Trace form

\( 716 q - 2 q^{2} + 8 q^{4} + 4 q^{8} + O(q^{10}) \) \( 716 q - 2 q^{2} + 8 q^{4} + 4 q^{8} + 4 q^{11} + 52 q^{16} - 4 q^{17} + 64 q^{19} + 20 q^{22} - 92 q^{26} - 4 q^{28} - 8 q^{31} + 8 q^{32} + 160 q^{34} - 56 q^{38} + 132 q^{43} - 300 q^{44} - 116 q^{46} - 4 q^{47} - 120 q^{52} - 4 q^{53} - 80 q^{56} + 288 q^{58} - 128 q^{59} - 68 q^{61} + 156 q^{62} + 176 q^{64} + 292 q^{67} - 336 q^{68} - 48 q^{73} + 456 q^{74} - 308 q^{76} + 192 q^{77} - 384 q^{82} - 44 q^{86} + 80 q^{88} - 388 q^{91} + 116 q^{92} - 680 q^{94} + 4 q^{97} + 578 q^{98} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)