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Properties

Label 2475.4.bq
Level $2475$
Weight $4$
Character orbit 2475.bq
Rep. character $\chi_{2475}(701,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $912$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2475.bq (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2475, [\chi])\).

Total New Old
Modular forms 4416 912 3504
Cusp forms 4224 912 3312
Eisenstein series 192 0 192

Trace form

\( 912 q - 912 q^{4} + O(q^{10}) \) \( 912 q - 912 q^{4} - 3552 q^{16} + 1188 q^{22} + 300 q^{28} + 900 q^{31} - 888 q^{34} + 456 q^{37} + 720 q^{46} + 12756 q^{49} - 8520 q^{52} - 216 q^{58} - 2280 q^{61} - 10872 q^{64} + 5232 q^{67} + 7020 q^{73} - 4080 q^{79} - 5100 q^{82} - 1176 q^{88} + 4056 q^{91} + 8520 q^{94} + 2784 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)