Space of modular forms of level 3025, weight 1, and Character 3025.r

• Label: 3025.1.r
• Level: $3025$
• Weight: $1$
• Character orbit: 3025.r
• Rep. character: $\chi_{3025}(844,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $330$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3025 = 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3025.r (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
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	52	36	16
Cusp forms	4	4	0
Eisenstein series	48	32	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 + q^4 + q^5 - q^9 - 5 * q^12 + 5 * q^15 - q^16 - q^20 - q^25 - 5 * q^27 + 2 * q^31 - 4 * q^36 + q^45 + q^49 - 5 * q^53 - 2 * q^59 + q^64 - 5 * q^67 + 5 * q^69 - 2 * q^71 + 5 * q^75 - 4 * q^80 - 6 * q^81 + 2 * q^89 - 5 * q^92 - 5 * q^93 + 5 * q^97

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3025.1.r.a	$3025$	$1$	3025.r	275.r	$10$	$4$	$1$	$1.510$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-11}) \)	None			✓	✓	275.1.s.a	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+(-\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\zeta_{10}q^{4}+\zeta_{10}^{3}q^{5}+\cdots\)