Space of modular forms of level 1575, weight 2, and Character 1575.d

• Label: 1575.2.d
• Level: $1575$
• Weight: $2$
• Character orbit: 1575.d
• Rep. character: $\chi_{1575}(1324,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $12$
• Sturm bound: $480$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1575.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(480\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

	Total	New	Old
Modular forms	264	46	218
Cusp forms	216	46	170
Eisenstein series	48	0	48

Trace form

\( 46 q - 56 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1575.2.d.a	$1575$	$2$	1575.d	5.b	$2$	$2$	$2$	$12.576$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}-iq^{7}+3iq^{8}-4q^{11}+\cdots\)
1575.2.d.b	$1575$	$2$	1575.d	5.b	$2$	$2$	$2$	$12.576$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}-iq^{7}+3iq^{8}-6iq^{13}+\cdots\)
1575.2.d.c	$1575$	$2$	1575.d	5.b	$2$	$2$	$2$	$12.576$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{4}-iq^{7}+3q^{11}+5iq^{13}+4q^{16}+\cdots\)
1575.2.d.d	$1575$	$2$	1575.d	5.b	$2$	$4$	$4$	$12.576$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-3q^{4}+\beta _{1}q^{7}+\beta _{2}q^{8}+(-2+\cdots)q^{11}+\cdots\)
1575.2.d.e	$1575$	$2$	1575.d	5.b	$2$	$4$	$4$	$12.576$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}+\beta _{2}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
1575.2.d.f	$1575$	$2$	1575.d	5.b	$2$	$4$	$4$	$12.576$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+3\beta _{2}q^{4}-\beta _{3}q^{7}+(-4\beta _{1}+\cdots)q^{8}+\cdots\)
1575.2.d.g	$1575$	$2$	1575.d	5.b	$2$	$4$	$4$	$12.576$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+\beta _{2}q^{7}+3\beta _{2}q^{8}+\cdots\)
1575.2.d.h	$1575$	$2$	1575.d	5.b	$2$	$4$	$4$	$12.576$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
1575.2.d.i	$1575$	$2$	1575.d	5.b	$2$	$4$	$4$	$12.576$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{2}q^{2}-q^{4}-\zeta_{12}q^{7}+\zeta_{12}^{2}q^{8}+\cdots\)
1575.2.d.j	$1575$	$2$	1575.d	5.b	$2$	$4$	$4$	$12.576$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
1575.2.d.k	$1575$	$2$	1575.d	5.b	$2$	$4$	$4$	$12.576$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{7}+(2\beta _{1}+\cdots)q^{8}+\cdots\)
1575.2.d.l	$1575$	$2$	1575.d	5.b	$2$	$8$	$8$	$12.576$	8.0.\(\cdots\).2	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(-2+\beta _{6})q^{4}-\beta _{4}q^{7}+(-2\beta _{2}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \)