Space of modular forms of level 500, weight 4, and Character 500.g

• Label: 500.4.g
• Level: $500$
• Weight: $4$
• Character orbit: 500.g
• Rep. character: $\chi_{500}(101,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $92$
• Newform subspaces: $2$
• Sturm bound: $300$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 500 = 2^{2} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	500.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(300\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(500, [\chi])\).

	Total	New	Old
Modular forms	960	92	868
Cusp forms	840	92	748
Eisenstein series	120	0	120

Trace form

92 * q + 4 * q^3 - 16 * q^7 - 257 * q^9 + 20 * q^11 + 86 * q^13 + 178 * q^17 - 2 * q^19 - 108 * q^21 - 102 * q^23 - 92 * q^27 + 68 * q^29 - 378 * q^31 - 560 * q^33 + 399 * q^37 - 592 * q^39 - 758 * q^41 + 180 * q^43 + 78 * q^47 + 5736 * q^49 + 1664 * q^51 + 657 * q^53 - 384 * q^57 - 144 * q^59 - 2176 * q^61 - 584 * q^63 + 134 * q^67 + 1084 * q^69 - 454 * q^71 + 1346 * q^73 - 2320 * q^77 - 896 * q^79 - 1507 * q^81 - 2082 * q^83 + 4316 * q^87 + 4857 * q^89 - 2212 * q^91 + 5664 * q^93 - 1156 * q^97 + 2980 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(500, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
500.4.g.a	$500$	$4$	500.g	25.d	$5$	$28$	$7$	$29.501$		None					100.4.g.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(-16\)		$\mathrm{SU}(2)[C_{5}]$
500.4.g.b	$500$	$4$	500.g	25.d	$5$	$64$	$16$	$29.501$		None			✓		100.4.i.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{4}^{\mathrm{old}}(500, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(500, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(250, [\chi])\)\(^{\oplus 2}\)