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Properties

Label 3025.1.f
Level $3025$
Weight $1$
Character orbit 3025.f
Rep. character $\chi_{3025}(243,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $6$
Newform subspaces $3$
Sturm bound $330$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 3025 = 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3025.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(330\)
Trace bound: \(2\)

Dimensions

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

Total New Old
Modular forms 82 24 58
Cusp forms 10 6 4
Eisenstein series 72 18 54

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q - 2 q^{3} + O(q^{10}) \) \( 6 q - 2 q^{3} + 2 q^{12} + 2 q^{16} + 2 q^{23} + 8 q^{26} - 6 q^{36} + 2 q^{37} - 2 q^{47} + 2 q^{48} + 2 q^{53} - 2 q^{67} - 4 q^{71} - 2 q^{81} + 8 q^{86} - 8 q^{91} - 2 q^{92} + 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.f.a 3025.f 5.c $2$ $1.510$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-55}) \) None \(-2\) \(0\) \(0\) \(2\) \(q+(-1-i)q^{2}+iq^{4}+(1+i)q^{7}-q^{8}+\cdots\)
3025.1.f.b 3025.f 5.c $2$ $1.510$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1+i)q^{3}-iq^{4}-iq^{9}+(1+i+\cdots)q^{12}+\cdots\)
3025.1.f.c 3025.f 5.c $2$ $1.510$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-55}) \) None \(2\) \(0\) \(0\) \(-2\) \(q+(1+i)q^{2}+iq^{4}+(-1-i)q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3025, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3025, [\chi]) \cong \)