Space of modular forms of level 150, weight 12, and Character 150.c

• Label: 150.12.c
• Level: $150$
• Weight: $12$
• Character orbit: 150.c
• Rep. character: $\chi_{150}(49,\cdot)$
• Character field: $\Q$
• Dimension: $34$
• Newform subspaces: $13$
• Sturm bound: $360$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	150.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(360\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(150, [\chi])\).

	Total	New	Old
Modular forms	342	34	308
Cusp forms	318	34	284
Eisenstein series	24	0	24

Trace form

34 * q - 34816 * q^4 + 15552 * q^6 - 2007666 * q^9 - 643104 * q^11 + 5074688 * q^14 + 35651584 * q^16 - 47820344 * q^19 + 1389960 * q^21 - 15925248 * q^24 - 33595520 * q^26 - 21334116 * q^29 + 867859424 * q^31 - 1215491712 * q^34 + 2055849984 * q^36 + 1027284444 * q^39 - 2671972620 * q^41 + 658538496 * q^44 - 5164651008 * q^46 - 2847569250 * q^49 + 5257708380 * q^51 - 918330048 * q^54 - 5196480512 * q^56 + 24457690080 * q^59 - 15648801364 * q^61 - 36507222016 * q^64 + 24280528896 * q^66 - 11404732608 * q^69 + 3993566976 * q^71 - 12802092928 * q^74 + 48968032256 * q^76 + 48922710208 * q^79 + 118550669634 * q^81 - 1423319040 * q^84 + 89763064576 * q^86 + 222038758908 * q^89 - 162658386512 * q^91 - 436740028416 * q^94 + 16307453952 * q^96 + 37974648096 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(150, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
150.12.c.a	$150$	$12$	150.c	5.b	$2$	$2$	$2$	$115.251$	\(\Q(\sqrt{-1}) \)	None					30.12.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+32 i q^{2}+243 i q^{3}-1024 q^{4}+\cdots\)
150.12.c.b	$150$	$12$	150.c	5.b	$2$	$2$	$2$	$115.251$	\(\Q(\sqrt{-1}) \)	None					6.12.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+32 i q^{2}+243 i q^{3}-1024 q^{4}+\cdots\)
150.12.c.c	$150$	$12$	150.c	5.b	$2$	$2$	$2$	$115.251$	\(\Q(\sqrt{-1}) \)	None					30.12.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-32 i q^{2}-243 i q^{3}-1024 q^{4}+\cdots\)
150.12.c.d	$150$	$12$	150.c	5.b	$2$	$2$	$2$	$115.251$	\(\Q(\sqrt{-1}) \)	None					30.12.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-32 i q^{2}-243 i q^{3}-1024 q^{4}+\cdots\)
150.12.c.e	$150$	$12$	150.c	5.b	$2$	$2$	$2$	$115.251$	\(\Q(\sqrt{-1}) \)	None					6.12.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+32 i q^{2}-243 i q^{3}-1024 q^{4}+\cdots\)
150.12.c.f	$150$	$12$	150.c	5.b	$2$	$2$	$2$	$115.251$	\(\Q(\sqrt{-1}) \)	None					6.12.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-32 i q^{2}+243 i q^{3}-1024 q^{4}+\cdots\)
150.12.c.g	$150$	$12$	150.c	5.b	$2$	$2$	$2$	$115.251$	\(\Q(\sqrt{-1}) \)	None					30.12.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+32 i q^{2}-243 i q^{3}-1024 q^{4}+\cdots\)
150.12.c.h	$150$	$12$	150.c	5.b	$2$	$2$	$2$	$115.251$	\(\Q(\sqrt{-1}) \)	None					30.12.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+32 i q^{2}-243 i q^{3}-1024 q^{4}+\cdots\)
150.12.c.i	$150$	$12$	150.c	5.b	$2$	$2$	$2$	$115.251$	\(\Q(\sqrt{-1}) \)	None					30.12.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+32 i q^{2}-243 i q^{3}-1024 q^{4}+\cdots\)
150.12.c.j	$150$	$12$	150.c	5.b	$2$	$4$	$4$	$115.251$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None		✓			150.12.a.m	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{5}\beta _{1}q^{2}+3^{5}\beta _{1}q^{3}-2^{10}q^{4}-6^{5}q^{6}+\cdots\)
150.12.c.k	$150$	$12$	150.c	5.b	$2$	$4$	$4$	$115.251$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		✓			150.12.a.n	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{5}\beta _{1}q^{2}+3^{5}\beta _{1}q^{3}-2^{10}q^{4}-6^{5}q^{6}+\cdots\)
150.12.c.l	$150$	$12$	150.c	5.b	$2$	$4$	$4$	$115.251$	\(\Q(i, \sqrt{499})\)	None		✓			150.12.a.l	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{5}\beta _{1}q^{2}-3^{5}\beta _{1}q^{3}-2^{10}q^{4}+6^{5}q^{6}+\cdots\)
150.12.c.m	$150$	$12$	150.c	5.b	$2$	$4$	$4$	$115.251$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		✓			150.12.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{5}\beta _{1}q^{2}-3^{5}\beta _{1}q^{3}-2^{10}q^{4}+6^{5}q^{6}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(150, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)