Space of modular forms of level 75, weight 4, and Character 75.b

• Label: 75.4.b
• Level: $75$
• Weight: $4$
• Character orbit: 75.b
• Rep. character: $\chi_{75}(49,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $40$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	75.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(40\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(75, [\chi])\).

	Total	New	Old
Modular forms	36	8	28
Cusp forms	24	8	16
Eisenstein series	12	0	12

Trace form

\( 8 q - 36 q^{4} - 24 q^{6} - 72 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(75, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
75.4.b.a	$75$	$4$	75.b	5.b	$2$	$2$	$2$	$4.425$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{2}+3iq^{3}-q^{4}-9q^{6}+20iq^{7}+\cdots\)
75.4.b.b	$75$	$4$	75.b	5.b	$2$	$2$	$2$	$4.425$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-3iq^{3}+7q^{4}+3q^{6}-24iq^{7}+\cdots\)
75.4.b.c	$75$	$4$	75.b	5.b	$2$	$4$	$4$	$4.425$	\(\Q(i, \sqrt{19})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{3})q^{2}-3\beta _{1}q^{3}+(-12+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(75, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(75, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)