Space of modular forms of level 150, weight 4, and Character 150.c

• Label: 150.4.c
• Level: $150$
• Weight: $4$
• Character orbit: 150.c
• Rep. character: $\chi_{150}(49,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $5$
• Sturm bound: $120$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	150.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(120\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(150, [\chi])\).

	Total	New	Old
Modular forms	102	10	92
Cusp forms	78	10	68
Eisenstein series	24	0	24

Trace form

\( 10 q - 40 q^{4} + 12 q^{6} - 90 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(150, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
150.4.c.a	$150$	$4$	150.c	5.b	$2$	$2$	$2$	$8.850$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}+3iq^{3}-4q^{4}-6q^{6}-2^{5}iq^{7}+\cdots\)
150.4.c.b	$150$	$4$	150.c	5.b	$2$	$2$	$2$	$8.850$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}+3iq^{3}-4q^{4}-6q^{6}+23iq^{7}+\cdots\)
150.4.c.c	$150$	$4$	150.c	5.b	$2$	$2$	$2$	$8.850$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-3iq^{3}-4q^{4}+6q^{6}-4iq^{7}+\cdots\)
150.4.c.d	$150$	$4$	150.c	5.b	$2$	$2$	$2$	$8.850$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-3iq^{3}-4q^{4}+6q^{6}+2^{4}iq^{7}+\cdots\)
150.4.c.e	$150$	$4$	150.c	5.b	$2$	$2$	$2$	$8.850$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-3iq^{3}-4q^{4}+6q^{6}+iq^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(150, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)