Space of modular forms of level 1075, weight 2, and Character 1075.b

• Label: 1075.2.b
• Level: $1075$
• Weight: $2$
• Character orbit: 1075.b
• Rep. character: $\chi_{1075}(474,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $11$
• Sturm bound: $220$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1075.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(220\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(2\), \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1075, [\chi])\).

	Total	New	Old
Modular forms	116	64	52
Cusp forms	104	64	40
Eisenstein series	12	0	12

Trace form

\( 64 q - 58 q^{4} - 4 q^{6} - 64 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1075, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1075.2.b.a	$1075$	$2$	1075.b	5.b	$2$	$2$	$2$	$8.584$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}+2iq^{3}-2q^{4}-4q^{6}+2iq^{7}+\cdots\)
1075.2.b.b	$1075$	$2$	1075.b	5.b	$2$	$2$	$2$	$8.584$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-2iq^{3}-2q^{4}+4q^{6}-q^{9}+\cdots\)
1075.2.b.c	$1075$	$2$	1075.b	5.b	$2$	$2$	$2$	$8.584$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+2iq^{3}+q^{4}-2q^{6}-4iq^{7}+\cdots\)
1075.2.b.d	$1075$	$2$	1075.b	5.b	$2$	$2$	$2$	$8.584$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}+2q^{4}+4iq^{7}-q^{9}+q^{11}+\cdots\)
1075.2.b.e	$1075$	$2$	1075.b	5.b	$2$	$2$	$2$	$8.584$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{4}+2iq^{7}+3q^{9}-q^{11}-iq^{13}+\cdots\)
1075.2.b.f	$1075$	$2$	1075.b	5.b	$2$	$4$	$4$	$8.584$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{2}+\zeta_{8}^{2}q^{3}-2q^{6}+(2\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
1075.2.b.g	$1075$	$2$	1075.b	5.b	$2$	$6$	$6$	$8.584$	6.0.6594624.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{4})q^{2}-\beta _{1}q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
1075.2.b.h	$1075$	$2$	1075.b	5.b	$2$	$10$	$10$	$8.584$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
1075.2.b.i	$1075$	$2$	1075.b	5.b	$2$	$10$	$10$	$8.584$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{3})q^{2}-\beta _{4}q^{3}+(\beta _{2}-\beta _{6}+\cdots)q^{4}+\cdots\)
1075.2.b.j	$1075$	$2$	1075.b	5.b	$2$	$12$	$12$	$8.584$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-2+\beta _{2})q^{4}+(2+\cdots)q^{6}+\cdots\)
1075.2.b.k	$1075$	$2$	1075.b	5.b	$2$	$12$	$12$	$8.584$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{7})q^{2}+(-\beta _{7}-\beta _{10})q^{3}+(-2+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1075, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1075, [\chi]) \cong \)