Space of modular forms of level 75, weight 11, and Character 75.d

• Label: 75.11.d
• Level: $75$
• Weight: $11$
• Character orbit: 75.d
• Rep. character: $\chi_{75}(74,\cdot)$
• Character field: $\Q$
• Dimension: $58$
• Newform subspaces: $4$
• Sturm bound: $110$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	75.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(110\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(75, [\chi])\).

	Total	New	Old
Modular forms	106	62	44
Cusp forms	94	58	36
Eisenstein series	12	4	8

Trace form

\( 58 q + 29896 q^{4} + 14206 q^{6} - 139648 q^{9} + O(q^{10}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(75, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
75.11.d.a	$75$	$11$	75.d	15.d	$2$	$2$	$2$	$47.652$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{5}iq^{3}-2^{10}q^{4}-32989iq^{7}+\cdots\)
75.11.d.b	$75$	$11$	75.d	15.d	$2$	$4$	$4$	$47.652$	\(\Q(i, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(-3^{3}\beta _{1}-9\beta _{3})q^{3}-304q^{4}+\cdots\)
75.11.d.c	$75$	$11$	75.d	15.d	$2$	$24$	$24$	$47.652$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
75.11.d.d	$75$	$11$	75.d	15.d	$2$	$28$	$28$	$47.652$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{11}^{\mathrm{old}}(75, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(75, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)