Space of modular forms of level 1025, weight 2, and Character 1025.b

• Label: 1025.2.b
• Level: $1025$
• Weight: $2$
• Character orbit: 1025.b
• Rep. character: $\chi_{1025}(124,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $11$
• Sturm bound: $210$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 1025 = 5^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1025.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(210\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1025, [\chi])\).

	Total	New	Old
Modular forms	112	60	52
Cusp forms	100	60	40
Eisenstein series	12	0	12

Trace form

\( 60 q - 52 q^{4} - 4 q^{6} - 56 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1025, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1025.2.b.a	$1025$	$2$	1025.b	5.b	$2$	$2$	$2$	$8.185$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+2iq^{3}+q^{4}-2q^{6}-2iq^{7}+\cdots\)
1025.2.b.b	$1025$	$2$	1025.b	5.b	$2$	$2$	$2$	$8.185$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+4iq^{7}+3iq^{8}+3q^{9}+\cdots\)
1025.2.b.c	$1025$	$2$	1025.b	5.b	$2$	$2$	$2$	$8.185$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-2iq^{3}+q^{4}+2q^{6}+2iq^{7}+\cdots\)
1025.2.b.d	$1025$	$2$	1025.b	5.b	$2$	$4$	$4$	$8.185$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+3\beta _{2}q^{3}+(-2+\beta _{3})q^{4}+\cdots\)
1025.2.b.e	$1025$	$2$	1025.b	5.b	$2$	$4$	$4$	$8.185$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(-2+\beta _{3})q^{4}+(4+\cdots)q^{6}+\cdots\)
1025.2.b.f	$1025$	$2$	1025.b	5.b	$2$	$4$	$4$	$8.185$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-\beta _{2}q^{6}+\cdots\)
1025.2.b.g	$1025$	$2$	1025.b	5.b	$2$	$6$	$6$	$8.185$	6.0.3356224.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{5})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{3}+\cdots\)
1025.2.b.h	$1025$	$2$	1025.b	5.b	$2$	$6$	$6$	$8.185$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{4}-\beta _{5})q^{2}-\beta _{5}q^{3}+(-1+2\beta _{2}+\cdots)q^{4}+\cdots\)
1025.2.b.i	$1025$	$2$	1025.b	5.b	$2$	$6$	$6$	$8.185$	6.0.3356224.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3}-\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1025.2.b.j	$1025$	$2$	1025.b	5.b	$2$	$10$	$10$	$8.185$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{2}+(-\beta _{1}-\beta _{6}+\beta _{8})q^{3}+(-2\beta _{2}+\cdots)q^{4}+\cdots\)
1025.2.b.k	$1025$	$2$	1025.b	5.b	$2$	$14$	$14$	$8.185$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{2}+\beta _{7}q^{3}+(-1-\beta _{11})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1025, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1025, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(205, [\chi])\)\(^{\oplus 2}\)