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 - 143976 * q^11 - 129152 * q^14 + 1703936 * q^16 + 462596 * q^19 + 37260 * q^21 + 663552 * q^24 - 5139520 * q^26 - 20580516 * q^29 - 10091204 * q^31 + 19286208 * q^34 + 43670016 * q^36 + 11915424 * q^39 + 61392300 * q^41 + 36857856 * q^44 - 91948032 * q^46 - 302388630 * q^49 - 63330660 * q^51 + 17006112 * q^54 + 33062912 * q^56 - 236502120 * q^59 - 269230616 * q^61 - 436207616 * q^64 - 69175296 * q^66 - 321492888 * q^69 + 157682304 * q^71 + 587363392 * q^74 - 118424576 * q^76 - 1572871792 * q^79 + 1119214746 * q^81 - 9538560 * q^84 - 753122176 * q^86 - 4879662012 * q^89 + 4047329852 * q^91 + 3778689024 * q^94 - 169869312 * q^96 + 944626536 * q^99

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	Largest	Maximal	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	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+16 i q^{2}+81 i q^{3}-256 q^{4}-1296 q^{6}+\cdots$
150.10.c.b	$150$	$10$	150.c	5.b	$2$	$2$	$2$	$77.255$	$\Q(\sqrt{-1})$	None					30.10.a.c	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-16 i q^{2}-81 i q^{3}-256 q^{4}-1296 q^{6}+\cdots$
150.10.c.c	$150$	$10$	150.c	5.b	$2$	$2$	$2$	$77.255$	$\Q(\sqrt{-1})$	None					30.10.a.e	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-16 i q^{2}-81 i q^{3}-256 q^{4}-1296 q^{6}+\cdots$
150.10.c.d	$150$	$10$	150.c	5.b	$2$	$2$	$2$	$77.255$	$\Q(\sqrt{-1})$	None					6.10.a.a	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+16 i q^{2}+81 i q^{3}-256 q^{4}-1296 q^{6}+\cdots$
150.10.c.e	$150$	$10$	150.c	5.b	$2$	$2$	$2$	$77.255$	$\Q(\sqrt{-1})$	None					30.10.a.d	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+16 i q^{2}+81 i q^{3}-256 q^{4}-1296 q^{6}+\cdots$
150.10.c.f	$150$	$10$	150.c	5.b	$2$	$2$	$2$	$77.255$	$\Q(\sqrt{-1})$	None					30.10.a.b	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+16 i q^{2}-81 i q^{3}-256 q^{4}+1296 q^{6}+\cdots$
150.10.c.g	$150$	$10$	150.c	5.b	$2$	$2$	$2$	$77.255$	$\Q(\sqrt{-1})$	None		✓			150.10.a.b	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-16 i q^{2}+81 i q^{3}-256 q^{4}+1296 q^{6}+\cdots$
150.10.c.h	$150$	$10$	150.c	5.b	$2$	$2$	$2$	$77.255$	$\Q(\sqrt{-1})$	None					30.10.a.a	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-16 i q^{2}+81 i q^{3}-256 q^{4}+1296 q^{6}+\cdots$
150.10.c.i	$150$	$10$	150.c	5.b	$2$	$2$	$2$	$77.255$	$\Q(\sqrt{-1})$	None					30.10.a.f	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+16 i q^{2}-81 i q^{3}-256 q^{4}+1296 q^{6}+\cdots$
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}$