Space of modular forms of level 150, weight 4, and Character 150.c

• Label: 150.4.c
• Level: $150$
• Weight: $4$
• Character orbit: 150.c
• Rep. character: $\chi_{150}(49,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $5$
• Sturm bound: $120$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	150.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(120\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(150, [\chi])\).

	Total	New	Old
Modular forms	102	10	92
Cusp forms	78	10	68
Eisenstein series	24	0	24

Trace form

10 * q - 40 * q^4 + 12 * q^6 - 90 * q^9 - 168 * q^11 - 16 * q^14 + 160 * q^16 - 236 * q^19 + 132 * q^21 - 48 * q^24 + 376 * q^26 + 396 * q^29 - 916 * q^31 + 24 * q^34 + 360 * q^36 + 192 * q^39 - 132 * q^41 + 672 * q^44 + 864 * q^46 - 222 * q^49 - 468 * q^51 - 108 * q^54 + 64 * q^56 - 1320 * q^59 - 2368 * q^61 - 640 * q^64 + 1152 * q^66 + 504 * q^69 + 1152 * q^71 + 1160 * q^74 + 944 * q^76 + 352 * q^79 + 810 * q^81 - 528 * q^84 - 2000 * q^86 + 2772 * q^89 - 1940 * q^91 - 1152 * q^94 + 192 * q^96 + 1512 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(150, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
150.4.c.a	$150$	$4$	150.c	5.b	$2$	$2$	$2$	$8.850$	\(\Q(\sqrt{-1}) \)	None					30.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+3 i q^{3}-4 q^{4}-6 q^{6}+\cdots\)
150.4.c.b	$150$	$4$	150.c	5.b	$2$	$2$	$2$	$8.850$	\(\Q(\sqrt{-1}) \)	None		✓			150.4.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+3 i q^{3}-4 q^{4}-6 q^{6}+\cdots\)
150.4.c.c	$150$	$4$	150.c	5.b	$2$	$2$	$2$	$8.850$	\(\Q(\sqrt{-1}) \)	None					30.4.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-3 i q^{3}-4 q^{4}+6 q^{6}+\cdots\)
150.4.c.d	$150$	$4$	150.c	5.b	$2$	$2$	$2$	$8.850$	\(\Q(\sqrt{-1}) \)	None					6.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-3 i q^{3}-4 q^{4}+6 q^{6}+\cdots\)
150.4.c.e	$150$	$4$	150.c	5.b	$2$	$2$	$2$	$8.850$	\(\Q(\sqrt{-1}) \)	None		✓			150.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-3 i q^{3}-4 q^{4}+6 q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

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