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

• Label: 150.11.f
• Level: $150$
• Weight: $11$
• Character orbit: 150.f
• Rep. character: $\chi_{150}(7,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $60$
• Newform subspaces: $8$
• Sturm bound: $330$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	150.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(330\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	624	60	564
Cusp forms	576	60	516
Eisenstein series	48	0	48

Trace form

\( 60 q - 64 q^{2} + 2816 q^{7} + 32768 q^{8} + O(q^{10}) \)

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.f.a	$150$	$11$	150.f	5.c	$4$	$4$	$2$	$95.304$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(-64\)	\(0\)	\(0\)	\(39816\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2^{4}+2^{4}\beta _{2})q^{2}-3^{4}\beta _{1}q^{3}-2^{9}\beta _{2}q^{4}+\cdots\)
150.11.f.b	$150$	$11$	150.f	5.c	$4$	$4$	$2$	$95.304$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(64\)	\(0\)	\(0\)	\(-39816\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2^{4}-2^{4}\beta _{2})q^{2}-3^{4}\beta _{1}q^{3}-2^{9}\beta _{2}q^{4}+\cdots\)
150.11.f.c	$150$	$11$	150.f	5.c	$4$	$8$	$4$	$95.304$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(-128\)	\(0\)	\(0\)	\(-30048\)	$2^{12}\cdot 3^{4}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2^{4}+2^{4}\beta _{1})q^{2}-3^{4}\beta _{3}q^{3}-2^{9}\beta _{1}q^{4}+\cdots\)
150.11.f.d	$150$	$11$	150.f	5.c	$4$	$8$	$4$	$95.304$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(-128\)	\(0\)	\(0\)	\(28512\)	$2^{14}\cdot 3^{14}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2^{4}-2^{4}\beta _{1})q^{2}-\beta _{2}q^{3}+2^{9}\beta _{1}q^{4}+\cdots\)
150.11.f.e	$150$	$11$	150.f	5.c	$4$	$8$	$4$	$95.304$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(128\)	\(0\)	\(0\)	\(-28512\)	$2^{14}\cdot 3^{14}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2^{4}-2^{4}\beta _{1})q^{2}+\beta _{3}q^{3}-2^{9}\beta _{1}q^{4}+\cdots\)
150.11.f.f	$150$	$11$	150.f	5.c	$4$	$8$	$4$	$95.304$	8.0.\(\cdots\).1	None		$2$	$0$	\(128\)	\(0\)	\(0\)	\(14168\)	$2^{12}\cdot 3^{12}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2^{4}-2^{4}\beta _{1})q^{2}+3\beta _{2}q^{3}-2^{9}\beta _{1}q^{4}+\cdots\)
150.11.f.g	$150$	$11$	150.f	5.c	$4$	$8$	$4$	$95.304$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(128\)	\(0\)	\(0\)	\(30048\)	$2^{12}\cdot 3^{4}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2^{4}-2^{4}\beta _{1})q^{2}+3^{4}\beta _{3}q^{3}-2^{9}\beta _{1}q^{4}+\cdots\)
150.11.f.h	$150$	$11$	150.f	5.c	$4$	$12$	$6$	$95.304$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-192\)	\(0\)	\(0\)	\(-11352\)	$2^{14}\cdot 3^{24}\cdot 5^{14}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2^{4}+2^{4}\beta _{1})q^{2}-\beta _{2}q^{3}-2^{9}\beta _{1}q^{4}+\cdots\)

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

\( S_{11}^{\mathrm{old}}(150, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)