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

• Label: 150.2.h
• Level: $150$
• Weight: $2$
• Character orbit: 150.h
• Rep. character: $\chi_{150}(19,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $60$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(60\)
Trace bound:			\(1\)
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	24	112
Cusp forms	104	24	80
Eisenstein series	32	0	32

Trace form

24 * q + 6 * q^4 + 4 * q^5 - 2 * q^6 + 6 * q^9 + 2 * q^10 + 12 * q^11 - 2 * q^15 - 6 * q^16 - 20 * q^17 - 8 * q^19 - 4 * q^20 - 4 * q^21 - 20 * q^22 - 20 * q^23 - 8 * q^24 + 14 * q^25 + 8 * q^26 - 10 * q^28 - 32 * q^29 - 16 * q^30 + 6 * q^31 - 20 * q^33 + 20 * q^34 - 24 * q^35 - 6 * q^36 - 2 * q^40 + 44 * q^41 + 10 * q^42 + 8 * q^44 - 4 * q^45 + 4 * q^46 - 40 * q^47 - 44 * q^49 - 8 * q^50 + 16 * q^51 + 2 * q^54 + 28 * q^55 + 12 * q^60 + 12 * q^61 + 60 * q^62 + 20 * q^63 + 6 * q^64 + 12 * q^65 - 8 * q^66 - 40 * q^67 + 16 * q^69 - 22 * q^70 - 8 * q^71 + 8 * q^74 + 8 * q^75 + 8 * q^76 + 80 * q^77 - 4 * q^79 + 4 * q^80 - 6 * q^81 + 40 * q^83 + 4 * q^84 + 16 * q^85 - 24 * q^86 - 20 * q^87 + 10 * q^88 + 36 * q^89 - 2 * q^90 - 12 * q^91 + 32 * q^94 - 2 * q^96 + 50 * q^97 + 80 * 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.h.a	$150$	$2$	150.h	25.e	$10$	$8$	$2$	$1.198$	\(\Q(\zeta_{20})\)	None		✓			150.2.h.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\zeta_{20}q^{2}-\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(\zeta_{20}+\cdots)q^{5}+\cdots\)
150.2.h.b	$150$	$2$	150.h	25.e	$10$	$16$	$4$	$1.198$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		150.2.h.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$5$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{8}q^{2}+\beta _{6}q^{3}-\beta _{10}q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots\)

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

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