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Properties

Label 3600.3.s
Level $3600$
Weight $3$
Character orbit 3600.s
Rep. character $\chi_{3600}(701,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $608$
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.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
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 608 2320
Cusp forms 2832 608 2224
Eisenstein series 96 0 96

Trace form

\( 608 q + O(q^{10}) \) \( 608 q - 64 q^{16} - 64 q^{19} + 136 q^{22} - 120 q^{28} + 248 q^{34} - 128 q^{43} - 88 q^{46} - 4256 q^{49} + 216 q^{52} - 248 q^{58} - 64 q^{61} + 48 q^{64} - 64 q^{67} - 128 q^{76} + 512 q^{79} + 320 q^{82} - 432 q^{88} - 192 q^{91} + 632 q^{94} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)