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Properties

Label 675.4.f
Level $675$
Weight $4$
Character orbit 675.f
Rep. character $\chi_{675}(107,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 675.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(675, [\chi])\).

Total New Old
Modular forms 576 144 432
Cusp forms 504 144 360
Eisenstein series 72 0 72

Trace form

\( 144 q + 12 q^{7} + O(q^{10}) \) \( 144 q + 12 q^{7} - 2760 q^{16} + 528 q^{22} - 288 q^{28} - 888 q^{31} - 1368 q^{37} + 1464 q^{43} + 888 q^{46} - 804 q^{52} - 5928 q^{58} - 2064 q^{61} + 816 q^{67} + 420 q^{73} - 1416 q^{76} - 1764 q^{82} + 10248 q^{88} + 11160 q^{91} + 1980 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(675, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(675, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(675, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)