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

• Label: 1575.2.bc
• Level: $1575$
• Weight: $2$
• Character orbit: 1575.bc
• Rep. character: $\chi_{1575}(899,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $5$
• 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.bc (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
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	528	96	432
Cusp forms	432	96	336
Eisenstein series	96	0	96

Trace form

\( 96 q - 48 q^{4} + O(q^{10}) \)

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.bc.a	$1575$	$2$	1575.bc	105.p	$6$	$8$	$4$	$12.576$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{2}+(3\zeta_{24}-2\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
1575.2.bc.b	$1575$	$2$	1575.bc	105.p	$6$	$8$	$4$	$12.576$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+2\zeta_{24}^{2}q^{4}+(2\zeta_{24}+\zeta_{24}^{3})q^{7}-\zeta_{24}^{5}q^{11}+\cdots\)
1575.2.bc.c	$1575$	$2$	1575.bc	105.p	$6$	$24$	$12$	$12.576$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
1575.2.bc.d	$1575$	$2$	1575.bc	105.p	$6$	$24$	$12$	$12.576$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
1575.2.bc.e	$1575$	$2$	1575.bc	105.p	$6$	$32$	$16$	$12.576$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)