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

• Label: 3025.1.bq
• Level: $3025$
• Weight: $1$
• Character orbit: 3025.bq
• Rep. character: $\chi_{3025}(3,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $8$
• 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.bq (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{20})\)
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	104	72	32
Cusp forms	8	8	0
Eisenstein series	96	64	32

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

8 * q - 2 * q^3 - 10 * q^9 + 2 * q^12 - 2 * q^15 + 2 * q^16 + 8 * q^20 + 2 * q^23 + 2 * q^25 - 8 * q^36 - 8 * q^37 - 2 * q^45 - 2 * q^47 + 2 * q^48 + 2 * q^53 - 2 * q^60 - 2 * q^67 + 6 * q^71 + 2 * q^75 + 8 * q^81 - 2 * q^92 - 10 * q^93 + 2 * 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.bq.a	$3025$	$1$	3025.bq	275.ap	$20$	$8$	$1$	$1.510$	\(\Q(\zeta_{20})\)	$D_{20}$	\(\Q(\sqrt{-11}) \)	None		✓	✓	✓	3025.1.bj.a	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{20}^{2}-\zeta_{20}^{5})q^{3}+\zeta_{20}^{3}q^{4}+\cdots\)