Properties

Label 2475.1.t
Level $2475$
Weight $1$
Character orbit 2475.t
Rep. character $\chi_{2475}(274,\cdot)$
Character field $\Q(\zeta_{6})$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 495 \)
Character field: \(\Q(\zeta_{6})\)
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 36 12 24
Cusp forms 12 4 8
Eisenstein series 24 8 16

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

\( 4 q + 2 q^{4} + 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{4} + 2 q^{9} - 2 q^{11} - 2 q^{16} + 2 q^{31} + 4 q^{36} - 4 q^{44} + 2 q^{49} - 2 q^{59} - 4 q^{64} + 4 q^{69} - 4 q^{71} - 2 q^{81} - 8 q^{89} + 2 q^{99} + O(q^{100}) \)

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.t.a 2475.t 495.o $4$ $1.235$ \(\Q(\zeta_{12})\) $D_{3}$ \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{2}q^{11}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)