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Properties

Label 3600.2.bd
Level $3600$
Weight $2$
Character orbit 3600.bd
Rep. character $\chi_{3600}(307,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $356$
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.bd (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 1488 364 1124
Cusp forms 1392 356 1036
Eisenstein series 96 8 88

Trace form

\( 356 q - 2 q^{2} - 8 q^{4} + 4 q^{7} + 4 q^{8} + O(q^{10}) \) \( 356 q - 2 q^{2} - 8 q^{4} + 4 q^{7} + 4 q^{8} + 4 q^{11} + 4 q^{13} - 12 q^{16} - 4 q^{17} + 16 q^{19} + 16 q^{22} - 4 q^{23} - 28 q^{26} - 16 q^{28} - 32 q^{32} + 32 q^{34} + 4 q^{37} - 12 q^{38} - 28 q^{43} + 44 q^{44} - 20 q^{46} + 24 q^{47} + 16 q^{52} + 16 q^{56} + 4 q^{58} + 32 q^{59} + 28 q^{61} + 60 q^{62} + 16 q^{64} - 20 q^{67} + 24 q^{68} - 56 q^{71} - 8 q^{73} + 32 q^{74} + 12 q^{76} + 36 q^{82} + 52 q^{86} + 32 q^{88} - 36 q^{91} + 32 q^{92} + 56 q^{94} + 4 q^{97} + 54 q^{98} + O(q^{100}) \)

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

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