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

• Label: 250.2.b
• Level: $250$
• Weight: $2$
• Character orbit: 250.b
• Rep. character: $\chi_{250}(249,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $75$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(75\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	48	8	40
Cusp forms	28	8	20
Eisenstein series	20	0	20

Trace form

8 * q - 8 * q^4 + 2 * q^6 - 14 * q^9 + 6 * q^11 - 4 * q^14 + 8 * q^16 + 30 * q^19 - 24 * q^21 - 2 * q^24 + 2 * q^26 - 10 * q^29 - 24 * q^31 - 4 * q^34 + 14 * q^36 + 12 * q^39 + 16 * q^41 - 6 * q^44 + 12 * q^46 + 4 * q^49 - 24 * q^51 + 40 * q^54 + 4 * q^56 + 30 * q^59 - 14 * q^61 - 8 * q^64 - 36 * q^66 - 28 * q^69 + 16 * q^71 - 14 * q^74 - 30 * q^76 + 48 * q^81 + 24 * q^84 - 38 * q^86 - 20 * q^89 - 24 * q^91 - 24 * q^94 + 2 * q^96 + 2 * 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.b.a	$250$	$2$	250.b	5.b	$2$	$4$	$4$	$1.996$	\(\Q(i, \sqrt{5})\)	None		✓			250.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+2\beta _{1}q^{3}-q^{4}+2\beta _{2}q^{6}+\cdots\)
250.2.b.b	$250$	$2$	250.b	5.b	$2$	$4$	$4$	$1.996$	\(\Q(i, \sqrt{5})\)	None		✓			250.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{3}-q^{4}+(1-\beta _{2}+\cdots)q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(250, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 2}\)