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Properties

Label 2475.1.bu
Level $2475$
Weight $1$
Character orbit 2475.bu
Rep. character $\chi_{2475}(406,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $4$
Newform subspaces $1$
Sturm bound $360$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2475.bu (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(360\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2475, [\chi])\).

Total New Old
Modular forms 48 12 36
Cusp forms 16 4 12
Eisenstein series 32 8 24

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q - q^{4} - 4 q^{5} + O(q^{10}) \) \( 4 q - q^{4} - 4 q^{5} + q^{11} - q^{16} + q^{20} + 2 q^{23} + 4 q^{25} - 2 q^{31} - 2 q^{37} + q^{44} + 2 q^{47} + 4 q^{49} + 2 q^{53} - q^{55} - 3 q^{59} - q^{64} + 3 q^{67} + 2 q^{71} + q^{80} + 2 q^{89} - 3 q^{92} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2475.1.bu.a 2475.bu 275.v $4$ $1.235$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{10}^{4}q^{4}-q^{5}-\zeta_{10}^{2}q^{11}-\zeta_{10}^{3}q^{16}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2475, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)