Space of modular forms of level 150, weight 3, and Character 150.b

• Label: 150.3.b
• Level: $150$
• Weight: $3$
• Character orbit: 150.b
• Rep. character: $\chi_{150}(149,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $90$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	150.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(90\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(150, [\chi])\).

	Total	New	Old
Modular forms	72	12	60
Cusp forms	48	12	36
Eisenstein series	24	0	24

Trace form

\( 12 q + 24 q^{4} + 8 q^{6} + 44 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(150, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
150.3.b.a	$150$	$3$	150.b	15.d	$2$	$4$	$4$	$4.087$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{3}q^{2}+(-\zeta_{8}-2\zeta_{8}^{3})q^{3}+2q^{4}+\cdots\)
150.3.b.b	$150$	$3$	150.b	15.d	$2$	$8$	$8$	$4.087$	8.0.40960000.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{3}q^{3}+2q^{4}+(-1-\beta _{4}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)