Space of modular forms of level 150, weight 2, and Character 150.g

• Label: 150.2.g
• Level: $150$
• Weight: $2$
• Character orbit: 150.g
• Rep. character: $\chi_{150}(31,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $60$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(60\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(150, [\chi])\).

	Total	New	Old
Modular forms	136	16	120
Cusp forms	104	16	88
Eisenstein series	32	0	32

Trace form

16 * q + 2 * q^2 - 4 * q^4 + 6 * q^5 + 2 * q^6 + 12 * q^7 + 2 * q^8 - 4 * q^9 + 4 * q^10 - 12 * q^11 + 12 * q^13 + 6 * q^15 - 4 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 4 * q^20 + 4 * q^21 - 8 * q^22 - 36 * q^23 - 8 * q^24 + 4 * q^25 + 12 * q^26 + 2 * q^28 - 12 * q^29 - 16 * q^30 - 6 * q^31 - 8 * q^32 - 8 * q^33 - 10 * q^34 + 16 * q^35 - 4 * q^36 + 26 * q^37 + 16 * q^38 + 4 * q^40 - 24 * q^41 - 6 * q^42 - 32 * q^43 + 8 * q^44 + 6 * q^45 - 4 * q^46 + 8 * q^47 - 4 * q^49 + 26 * q^50 - 16 * q^51 + 12 * q^52 - 30 * q^53 + 2 * q^54 - 40 * q^55 + 24 * q^57 + 24 * q^58 - 4 * q^60 + 8 * q^61 - 20 * q^62 - 8 * q^63 - 4 * q^64 + 62 * q^65 + 8 * q^66 + 32 * q^67 + 12 * q^68 + 16 * q^69 - 6 * q^70 + 8 * q^71 + 2 * q^72 - 8 * q^73 + 28 * q^74 + 24 * q^75 - 8 * q^76 + 16 * q^77 + 16 * q^78 - 4 * q^79 + 6 * q^80 - 4 * q^81 - 44 * q^82 - 8 * q^83 + 4 * q^84 - 14 * q^85 + 24 * q^86 + 16 * q^87 + 2 * q^88 + 6 * q^89 + 4 * q^90 + 12 * q^91 + 24 * q^92 - 16 * q^93 + 32 * q^94 + 16 * q^95 + 2 * q^96 + 26 * q^97 - 14 * q^98 + 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(150, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
150.2.g.a	$150$	$2$	150.g	25.d	$5$	$4$	$1$	$1.198$	\(\Q(\zeta_{10})\)	None		✓			150.2.g.a	$2$	$0$	\(-1\)	\(1\)	\(5\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
150.2.g.b	$150$	$2$	150.g	25.d	$5$	$4$	$1$	$1.198$	\(\Q(\zeta_{10})\)	None		✓			150.2.g.b	$2$	$0$	\(1\)	\(1\)	\(5\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+\cdots\)
150.2.g.c	$150$	$2$	150.g	25.d	$5$	$8$	$2$	$1.198$	8.0.1064390625.3	None		✓	✓		150.2.g.c	$2$	$0$	\(2\)	\(-2\)	\(-4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{2}q^{2}+\beta _{5}q^{3}+\beta _{5}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

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