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Properties

Label 3600.2.bc
Level $3600$
Weight $2$
Character orbit 3600.bc
Rep. character $\chi_{3600}(2357,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $288$
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.bc (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 240 \)
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 288 1200
Cusp forms 1392 288 1104
Eisenstein series 96 0 96

Trace form

\( 288 q - 16 q^{4} + O(q^{10}) \) \( 288 q - 16 q^{4} - 16 q^{16} - 32 q^{19} - 16 q^{22} - 32 q^{28} + 16 q^{34} - 64 q^{43} - 16 q^{46} + 24 q^{52} + 80 q^{58} - 64 q^{61} - 16 q^{64} - 16 q^{76} - 32 q^{88} - 80 q^{94} + O(q^{100}) \)

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

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