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

• Label: 150.4.g
• Level: $150$
• Weight: $4$
• Character orbit: 150.g
• Rep. character: $\chi_{150}(31,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $64$
• Newform subspaces: $4$
• Sturm bound: $120$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(120\)
Trace bound:			\(2\)
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	64	312
Cusp forms	344	64	280
Eisenstein series	32	0	32

Trace form

64 * q + 4 * q^2 - 64 * q^4 - 6 * q^5 - 12 * q^6 + 4 * q^7 + 16 * q^8 - 144 * q^9 + 32 * q^10 - 168 * q^11 - 44 * q^13 + 18 * q^15 - 256 * q^16 - 316 * q^17 - 144 * q^18 - 148 * q^19 - 224 * q^20 - 84 * q^21 + 384 * q^22 + 612 * q^23 + 192 * q^24 - 316 * q^25 - 72 * q^26 + 136 * q^28 + 108 * q^29 - 96 * q^30 - 414 * q^31 - 256 * q^32 - 564 * q^33 - 500 * q^34 - 1804 * q^35 - 576 * q^36 - 678 * q^37 - 352 * q^38 + 128 * q^40 + 924 * q^41 - 612 * q^42 + 1344 * q^43 + 448 * q^44 - 54 * q^45 - 1016 * q^46 + 2056 * q^47 + 4716 * q^49 - 428 * q^50 + 816 * q^51 - 176 * q^52 - 2310 * q^53 - 108 * q^54 + 3508 * q^55 - 72 * q^57 - 288 * q^58 - 1800 * q^59 - 768 * q^60 + 2352 * q^61 + 2120 * q^62 - 324 * q^63 - 1024 * q^64 - 698 * q^65 - 528 * q^66 - 2456 * q^67 + 1296 * q^68 + 696 * q^69 + 2308 * q^70 - 2168 * q^71 + 144 * q^72 + 4456 * q^73 + 1688 * q^74 - 792 * q^75 + 1408 * q^76 + 4352 * q^77 - 672 * q^78 + 3716 * q^79 - 96 * q^80 - 1296 * q^81 + 2472 * q^82 + 3596 * q^83 - 336 * q^84 - 6354 * q^85 + 336 * q^86 - 1608 * q^87 - 1584 * q^88 - 4074 * q^89 + 288 * q^90 + 5008 * q^91 - 1632 * q^92 + 1632 * q^93 - 1408 * q^94 - 3640 * q^95 - 192 * q^96 + 5242 * q^97 + 8228 * 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.g.a	$150$	$4$	150.g	25.d	$5$	$12$	$3$	$8.850$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			150.4.g.a	$2$	$0$	\(-6\)	\(9\)	\(-10\)	\(-44\)	$5^{3}$	$\mathrm{SU}(2)[C_{5}]$	\(q-2\beta _{1}q^{2}+(3-3\beta _{1}+3\beta _{3}+3\beta _{5}+\cdots)q^{3}+\cdots\)
150.4.g.b	$150$	$4$	150.g	25.d	$5$	$16$	$4$	$8.850$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			150.4.g.b	$2$	$0$	\(-8\)	\(-12\)	\(15\)	\(46\)	$5^{4}$	$\mathrm{SU}(2)[C_{5}]$	\(q-2\beta _{6}q^{2}+(-3+3\beta _{4}+3\beta _{5}+3\beta _{6}+\cdots)q^{3}+\cdots\)
150.4.g.c	$150$	$4$	150.g	25.d	$5$	$16$	$4$	$8.850$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			150.4.g.c	$2$	$0$	\(8\)	\(-12\)	\(5\)	\(12\)	$2^{4}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(2-2\beta _{1}+2\beta _{2}-2\beta _{3})q^{2}-3\beta _{1}q^{3}+\cdots\)
150.4.g.d	$150$	$4$	150.g	25.d	$5$	$20$	$5$	$8.850$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		150.4.g.d	$2$	$0$	\(10\)	\(15\)	\(-16\)	\(-10\)	$2^{4}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{5}]$	\(q-2\beta _{3}q^{2}+3\beta _{5}q^{3}-4\beta _{5}q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)

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

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