Space of modular forms of level 250, weight 2, and Character 250.h

• Label: 250.2.h
• Level: $250$
• Weight: $2$
• Character orbit: 250.h
• Rep. character: $\chi_{250}(9,\cdot)$
• Character field: $\Q(\zeta_{50})$
• Dimension: $240$
• Newform subspaces: $1$
• Sturm bound: $75$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.h (of order \(50\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 125 \)
Character field:			\(\Q(\zeta_{50})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(75\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(250, [\chi])\).

	Total	New	Old
Modular forms	800	240	560
Cusp forms	720	240	480
Eisenstein series	80	0	80

Trace form

240 * q + 10 * q^5 + 10 * q^11 - 40 * q^12 + 20 * q^15 - 10 * q^17 - 20 * q^19 - 20 * q^22 - 60 * q^23 - 10 * q^24 - 110 * q^25 + 30 * q^26 - 10 * q^28 - 20 * q^29 - 20 * q^30 + 10 * q^31 + 30 * q^33 - 10 * q^35 + 10 * q^37 - 20 * q^39 + 30 * q^41 + 10 * q^42 - 160 * q^45 + 20 * q^46 - 220 * q^47 + 10 * q^48 + 40 * q^49 + 20 * q^51 + 10 * q^55 - 30 * q^59 - 50 * q^60 + 40 * q^61 - 20 * q^63 - 50 * q^65 - 10 * q^67 - 20 * q^69 - 50 * q^71 - 50 * q^74 - 10 * q^75 + 10 * q^76 - 40 * q^77 - 170 * q^78 - 40 * q^79 + 50 * q^81 - 200 * q^82 - 50 * q^83 - 30 * q^84 + 20 * q^85 - 20 * q^87 + 10 * q^88 - 40 * q^89 + 30 * q^90 - 240 * q^91 + 10 * q^92 - 100 * q^93 - 100 * q^95 + 20 * q^97 + 40 * q^98 - 30 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(250, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
250.2.h.a	$250$	$2$	250.h	125.h	$50$	$240$	$12$	$1.996$		None		✓	✓	✓	250.2.h.a	$2$	$0$	\(0\)	\(0\)	\(10\)	\(0\)		$\mathrm{SU}(2)[C_{50}]$

Decomposition of \(S_{2}^{\mathrm{old}}(250, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(250, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 2}\)