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

• Label: 150.11.d
• Level: $150$
• Weight: $11$
• Character orbit: 150.d
• Rep. character: $\chi_{150}(101,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $5$
• Sturm bound: $330$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	150.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(330\)
Trace bound:			\(3\)
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	64	248
Cusp forms	288	64	224
Eisenstein series	24	0	24

Trace form

\( 64 q - 40 q^{3} - 32768 q^{4} - 6784 q^{6} - 26720 q^{7} - 148408 q^{9} + O(q^{10}) \)

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.d.a	$150$	$11$	150.d	3.b	$2$	$4$	$4$	$95.304$	\(\Q(\sqrt{-2}, \sqrt{85})\)	None		$2$	$0$	\(0\)	\(-84\)	\(0\)	\(45112\)	$2^{11}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-21-3\beta _{1}+\beta _{2})q^{3}-2^{9}q^{4}+\cdots\)
150.11.d.b	$150$	$11$	150.d	3.b	$2$	$12$	$12$	$95.304$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(44\)	\(0\)	\(-71832\)	$2^{28}\cdot 3^{18}\cdot 5^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+(4-\beta _{3}-\beta _{4})q^{3}-2^{9}q^{4}+\cdots\)
150.11.d.c	$150$	$11$	150.d	3.b	$2$	$14$	$14$	$95.304$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(-22\)	\(0\)	\(28466\)	$2^{35}\cdot 3^{29}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{1}-\beta _{2})q^{3}-2^{9}q^{4}+\cdots\)
150.11.d.d	$150$	$11$	150.d	3.b	$2$	$14$	$14$	$95.304$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(22\)	\(0\)	\(-28466\)	$2^{35}\cdot 3^{29}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(2-\beta _{1}+\beta _{2})q^{3}-2^{9}q^{4}+\cdots\)
150.11.d.e	$150$	$11$	150.d	3.b	$2$	$20$	$20$	$95.304$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{70}\cdot 3^{32}\cdot 5^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{10}q^{2}+(-\beta _{10}-\beta _{11})q^{3}-2^{9}q^{4}+\cdots\)

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

\( S_{11}^{\mathrm{old}}(150, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)