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

• Label: 150.4.h
• Level: $150$
• Weight: $4$
• Character orbit: 150.h
• Rep. character: $\chi_{150}(19,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $56$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	150.h (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	376	56	320
Cusp forms	344	56	288
Eisenstein series	32	0	32

Trace form

56 * q + 56 * q^4 - 4 * q^5 + 12 * q^6 + 126 * q^9 + 44 * q^10 + 168 * q^11 + 66 * q^15 - 224 * q^16 - 640 * q^17 - 148 * q^19 + 256 * q^20 + 84 * q^21 + 360 * q^22 + 740 * q^23 + 192 * q^24 + 714 * q^25 - 368 * q^26 + 120 * q^28 + 368 * q^29 - 96 * q^30 + 414 * q^31 - 960 * q^33 - 440 * q^34 - 1764 * q^35 - 504 * q^36 - 700 * q^37 - 176 * q^40 - 464 * q^41 + 1020 * q^42 + 448 * q^44 + 36 * q^45 + 1016 * q^46 + 1720 * q^47 - 1164 * q^49 + 176 * q^50 - 816 * q^51 + 5100 * q^53 - 108 * q^54 - 2280 * q^55 - 1800 * q^59 + 576 * q^60 - 692 * q^61 - 3480 * q^62 + 360 * q^63 + 896 * q^64 - 2448 * q^65 + 528 * q^66 + 720 * q^67 + 696 * q^69 + 2084 * q^70 + 2168 * q^71 + 600 * q^73 - 752 * q^74 + 264 * q^75 - 1408 * q^76 - 2240 * q^77 + 3716 * q^79 - 64 * q^80 - 1134 * q^81 - 8380 * q^83 - 336 * q^84 + 1856 * q^85 - 336 * q^86 - 1140 * q^87 + 1680 * q^88 + 936 * q^89 - 396 * q^90 - 5008 * q^91 - 1408 * q^94 + 11016 * q^95 + 192 * q^96 - 4350 * q^97 - 6560 * q^98 + 1008 * 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.h.a	$150$	$4$	150.h	25.e	$10$	$24$	$6$	$8.850$		None		✓			150.4.h.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
150.4.h.b	$150$	$4$	150.h	25.e	$10$	$32$	$8$	$8.850$		None		✓	✓		150.4.h.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

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