Properties

Label 3025.1.x
Level $3025$
Weight $1$
Character orbit 3025.x
Rep. character $\chi_{3025}(1201,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $4$
Newform subspaces $1$
Sturm bound $330$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3025 = 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3025.x (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(330\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3025, [\chi])\).

Total New Old
Modular forms 148 52 96
Cusp forms 4 4 0
Eisenstein series 144 48 96

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

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

Decomposition of \(S_{1}^{\mathrm{new}}(3025, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3025.1.x.a 3025.x 11.d $4$ $1.510$ \(\Q(\zeta_{10})\) $D_{2}$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{10}^{3}q^{4}-\zeta_{10}^{4}q^{9}-\zeta_{10}q^{16}+\cdots\)