Space of modular forms of level 150, weight 10, and Character 150.c

• Label: 150.10.c
• Level: $150$
• Weight: $10$
• Character orbit: 150.c
• Rep. character: $\chi_{150}(49,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $11$
• Sturm bound: $300$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	150.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(300\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(150, [\chi])\).

	Total	New	Old
Modular forms	282	26	256
Cusp forms	258	26	232
Eisenstein series	24	0	24

Trace form

\( 26 q - 6656 q^{4} - 2592 q^{6} - 170586 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(150, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
150.10.c.a	$150$	$10$	150.c	5.b	$2$	$2$	$2$	$77.255$	\(\Q(\sqrt{-1}) \)	None		✓	150.10.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{4}iq^{2}+3^{4}iq^{3}-2^{8}q^{4}-6^{4}q^{6}+\cdots\)
150.10.c.b	$150$	$10$	150.c	5.b	$2$	$2$	$2$	$77.255$	\(\Q(\sqrt{-1}) \)	None			30.10.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2^{4}iq^{2}-3^{4}iq^{3}-2^{8}q^{4}-6^{4}q^{6}+\cdots\)
150.10.c.c	$150$	$10$	150.c	5.b	$2$	$2$	$2$	$77.255$	\(\Q(\sqrt{-1}) \)	None			30.10.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2^{4}iq^{2}-3^{4}iq^{3}-2^{8}q^{4}-6^{4}q^{6}+\cdots\)
150.10.c.d	$150$	$10$	150.c	5.b	$2$	$2$	$2$	$77.255$	\(\Q(\sqrt{-1}) \)	None			6.10.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{4}iq^{2}+3^{4}iq^{3}-2^{8}q^{4}-6^{4}q^{6}+\cdots\)
150.10.c.e	$150$	$10$	150.c	5.b	$2$	$2$	$2$	$77.255$	\(\Q(\sqrt{-1}) \)	None			30.10.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{4}iq^{2}+3^{4}iq^{3}-2^{8}q^{4}-6^{4}q^{6}+\cdots\)
150.10.c.f	$150$	$10$	150.c	5.b	$2$	$2$	$2$	$77.255$	\(\Q(\sqrt{-1}) \)	None			30.10.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{4}iq^{2}-3^{4}iq^{3}-2^{8}q^{4}+6^{4}q^{6}+\cdots\)
150.10.c.g	$150$	$10$	150.c	5.b	$2$	$2$	$2$	$77.255$	\(\Q(\sqrt{-1}) \)	None		✓	150.10.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2^{4}iq^{2}+3^{4}iq^{3}-2^{8}q^{4}+6^{4}q^{6}+\cdots\)
150.10.c.h	$150$	$10$	150.c	5.b	$2$	$2$	$2$	$77.255$	\(\Q(\sqrt{-1}) \)	None			30.10.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2^{4}iq^{2}+3^{4}iq^{3}-2^{8}q^{4}+6^{4}q^{6}+\cdots\)
150.10.c.i	$150$	$10$	150.c	5.b	$2$	$2$	$2$	$77.255$	\(\Q(\sqrt{-1}) \)	None			30.10.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{4}iq^{2}-3^{4}iq^{3}-2^{8}q^{4}+6^{4}q^{6}+\cdots\)
150.10.c.j	$150$	$10$	150.c	5.b	$2$	$4$	$4$	$77.255$	\(\Q(i, \sqrt{274})\)	None		✓	150.10.a.m	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{4}\beta _{1}q^{2}+3^{4}\beta _{1}q^{3}-2^{8}q^{4}-6^{4}q^{6}+\cdots\)
150.10.c.k	$150$	$10$	150.c	5.b	$2$	$4$	$4$	$77.255$	\(\Q(i, \sqrt{6679})\)	None		✓	150.10.a.l	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{4}\beta _{1}q^{2}-3^{4}\beta _{1}q^{3}-2^{8}q^{4}+6^{4}q^{6}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

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