Space of modular forms of level 150, weight 16, and Character 150.c

• Label: 150.16.c
• Level: $150$
• Weight: $16$
• Character orbit: 150.c
• Rep. character: $\chi_{150}(49,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $15$
• Sturm bound: $480$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	150.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(480\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(150, [\chi])\).

	Total	New	Old
Modular forms	462	46	416
Cusp forms	438	46	392
Eisenstein series	24	0	24

Trace form

46 * q - 753664 * q^4 + 559872 * q^6 - 220016574 * q^9 + 249696888 * q^11 - 567649280 * q^14 + 12348030976 * q^16 + 9157571092 * q^19 + 9382431204 * q^21 - 9172942848 * q^24 - 154619196928 * q^26 - 336977054172 * q^29 + 236852300444 * q^31 + 160111188480 * q^34 + 3604751548416 * q^36 - 281352126240 * q^39 + 7217457182916 * q^41 - 4091033812992 * q^44 + 19178059677696 * q^46 - 42424430566194 * q^49 + 18267987844044 * q^51 - 2677850419968 * q^54 + 9300365803520 * q^56 + 68011347861240 * q^59 + 157290944290568 * q^61 - 202310139510784 * q^64 - 20748551749632 * q^66 - 102816307389384 * q^69 - 547980723453312 * q^71 + 263495685334528 * q^74 - 150037644771328 * q^76 + 657013541819056 * q^79 + 1052332452928206 * q^81 - 153721752846336 * q^84 - 1168232024329216 * q^86 + 1404131886881676 * q^89 - 113131215141428 * q^91 - 1607385987514368 * q^94 + 150289495621632 * q^96 - 1194292474700472 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(150, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
150.16.c.a	$150$	$16$	150.c	5.b	$2$	$2$	$2$	$214.040$	\(\Q(\sqrt{-1}) \)	None					6.16.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-128 i q^{2}-2187 i q^{3}-16384 q^{4}+\cdots\)
150.16.c.b	$150$	$16$	150.c	5.b	$2$	$2$	$2$	$214.040$	\(\Q(\sqrt{-1}) \)	None					30.16.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+128 i q^{2}+2187 i q^{3}-16384 q^{4}+\cdots\)
150.16.c.c	$150$	$16$	150.c	5.b	$2$	$2$	$2$	$214.040$	\(\Q(\sqrt{-1}) \)	None					30.16.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-128 i q^{2}-2187 i q^{3}-16384 q^{4}+\cdots\)
150.16.c.d	$150$	$16$	150.c	5.b	$2$	$2$	$2$	$214.040$	\(\Q(\sqrt{-1}) \)	None					30.16.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-128 i q^{2}-2187 i q^{3}-16384 q^{4}+\cdots\)
150.16.c.e	$150$	$16$	150.c	5.b	$2$	$2$	$2$	$214.040$	\(\Q(\sqrt{-1}) \)	None					30.16.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+128 i q^{2}-2187 i q^{3}-16384 q^{4}+\cdots\)
150.16.c.f	$150$	$16$	150.c	5.b	$2$	$2$	$2$	$214.040$	\(\Q(\sqrt{-1}) \)	None					30.16.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-128 i q^{2}+2187 i q^{3}-16384 q^{4}+\cdots\)
150.16.c.g	$150$	$16$	150.c	5.b	$2$	$2$	$2$	$214.040$	\(\Q(\sqrt{-1}) \)	None					30.16.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+128 i q^{2}-2187 i q^{3}-16384 q^{4}+\cdots\)
150.16.c.h	$150$	$16$	150.c	5.b	$2$	$2$	$2$	$214.040$	\(\Q(\sqrt{-1}) \)	None					6.16.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+128 i q^{2}-2187 i q^{3}-16384 q^{4}+\cdots\)
150.16.c.i	$150$	$16$	150.c	5.b	$2$	$2$	$2$	$214.040$	\(\Q(\sqrt{-1}) \)	None					6.16.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-128 i q^{2}+2187 i q^{3}-16384 q^{4}+\cdots\)
150.16.c.j	$150$	$16$	150.c	5.b	$2$	$4$	$4$	$214.040$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None		✓			150.16.a.o	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2^{7}\beta _{1}q^{2}-3^{7}\beta _{1}q^{3}-2^{14}q^{4}-6^{7}q^{6}+\cdots\)
150.16.c.k	$150$	$16$	150.c	5.b	$2$	$4$	$4$	$214.040$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None					30.16.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{4}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2^{7}\beta _{1}q^{2}-3^{7}\beta _{1}q^{3}-2^{14}q^{4}-6^{7}q^{6}+\cdots\)
150.16.c.l	$150$	$16$	150.c	5.b	$2$	$4$	$4$	$214.040$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None		✓			150.16.a.m	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{7}\beta _{1}q^{2}-3^{7}\beta _{1}q^{3}-2^{14}q^{4}+6^{7}q^{6}+\cdots\)
150.16.c.m	$150$	$16$	150.c	5.b	$2$	$4$	$4$	$214.040$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None					30.16.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{4}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{7}\beta _{1}q^{2}-3^{7}\beta _{1}q^{3}-2^{14}q^{4}+6^{7}q^{6}+\cdots\)
150.16.c.n	$150$	$16$	150.c	5.b	$2$	$6$	$6$	$214.040$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		✓			150.16.a.u	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{6}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2^{7}\beta _{1}q^{2}-3^{7}\beta _{1}q^{3}-2^{14}q^{4}-6^{7}q^{6}+\cdots\)
150.16.c.o	$150$	$16$	150.c	5.b	$2$	$6$	$6$	$214.040$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		✓			150.16.a.t	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{6}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2^{7}\beta _{1}q^{2}+3^{7}\beta _{1}q^{3}-2^{14}q^{4}+6^{7}q^{6}+\cdots\)

Decomposition of \(S_{16}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{16}^{\mathrm{old}}(150, [\chi]) \simeq \) \(S_{16}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)