Space of modular forms of level 150, weight 11, and Character 150.b

• Label: 150.11.b
• Level: $150$
• Weight: $11$
• Character orbit: 150.b
• Rep. character: $\chi_{150}(149,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $3$
• Sturm bound: $330$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	150.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(330\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(150, [\chi])\).

	Total	New	Old
Modular forms	312	60	252
Cusp forms	288	60	228
Eisenstein series	24	0	24

Trace form

\( 60 q + 30720 q^{4} - 12160 q^{6} + 189620 q^{9} + O(q^{10}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(150, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
150.11.b.a	$150$	$11$	150.b	15.d	$2$	$8$	$8$	$95.304$	8.0.\(\cdots\).10	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{26}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(10\beta _{1}+3\beta _{3}-\beta _{4})q^{3}+2^{9}q^{4}+\cdots\)
150.11.b.b	$150$	$11$	150.b	15.d	$2$	$24$	$24$	$95.304$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
150.11.b.c	$150$	$11$	150.b	15.d	$2$	$28$	$28$	$95.304$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{11}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(150, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)