Space of modular forms of level 150, weight 7, and Character 150.b

• Label: 150.7.b
• Level: $150$
• Weight: $7$
• Character orbit: 150.b
• Rep. character: $\chi_{150}(149,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $3$
• Sturm bound: $210$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
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:			\(210\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(150, [\chi])\).

	Total	New	Old
Modular forms	192	36	156
Cusp forms	168	36	132
Eisenstein series	24	0	24

Trace form

\( 36 q + 1152 q^{4} + 224 q^{6} - 208 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(150, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
150.7.b.a	$150$	$7$	150.b	15.d	$2$	$4$	$4$	$34.508$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{3}q^{2}+(-21\zeta_{8}-3\zeta_{8}^{3})q^{3}+2^{5}q^{4}+\cdots\)
150.7.b.b	$150$	$7$	150.b	15.d	$2$	$16$	$16$	$34.508$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{20}\cdot 3^{14}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{4}q^{3}+2^{5}q^{4}+(4+\beta _{8}+\cdots)q^{6}+\cdots\)
150.7.b.c	$150$	$7$	150.b	15.d	$2$	$16$	$16$	$34.508$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{28}\cdot 3^{12}\cdot 5^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+2^{5}q^{4}+(34+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(150, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)