Space of modular forms of level 125, weight 4, and Character 125.b

• Label: 125.4.b
• Level: $125$
• Weight: $4$
• Character orbit: 125.b
• Rep. character: $\chi_{125}(124,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $50$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	125.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(50\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(125, [\chi])\).

	Total	New	Old
Modular forms	42	24	18
Cusp forms	32	24	8
Eisenstein series	10	0	10

Trace form

24 * q - 102 * q^4 - 2 * q^6 - 218 * q^9 + 18 * q^11 - 4 * q^14 + 394 * q^16 + 310 * q^19 - 232 * q^21 - 70 * q^24 - 32 * q^26 + 90 * q^29 + 308 * q^31 + 26 * q^34 + 1064 * q^36 - 856 * q^39 + 128 * q^41 + 2436 * q^44 - 2062 * q^46 - 2732 * q^49 - 2792 * q^51 + 2010 * q^54 - 290 * q^56 + 1130 * q^59 + 2318 * q^61 - 2732 * q^64 + 186 * q^66 + 704 * q^69 - 412 * q^71 - 2914 * q^74 - 5230 * q^76 + 4740 * q^79 + 2444 * q^81 + 3036 * q^84 + 7578 * q^86 - 680 * q^89 + 1688 * q^91 + 5466 * q^94 - 5272 * q^96 - 5726 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(125, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
125.4.b.a	$125$	$4$	125.b	5.b	$2$	$4$	$4$	$7.375$	\(\Q(\sqrt{-6 + \sqrt{5}})\)	None		✓			125.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(1+2\beta _{2})q^{4}+\cdots\)
125.4.b.b	$125$	$4$	125.b	5.b	$2$	$8$	$8$	$7.375$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓			125.4.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+\beta _{4}q^{3}+(-5-\beta _{3})q^{4}+(5+\cdots)q^{6}+\cdots\)
125.4.b.c	$125$	$4$	125.b	5.b	$2$	$12$	$12$	$7.375$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓		125.4.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+\beta _{5}q^{3}+(-6-\beta _{2})q^{4}+(-3+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(125, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(125, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)