Space of modular forms of level 25, weight 8, and Character 25.b

• Label: 25.8.b
• Level: $25$
• Weight: $8$
• Character orbit: 25.b
• Rep. character: $\chi_{25}(24,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $3$
• Sturm bound: $20$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(20\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(25, [\chi])\).

	Total	New	Old
Modular forms	20	12	8
Cusp forms	14	10	4
Eisenstein series	6	2	4

Trace form

10 * q - 690 * q^4 + 1210 * q^6 - 6790 * q^9 + 18120 * q^11 + 2460 * q^14 + 66690 * q^16 - 62040 * q^19 - 113400 * q^21 + 74130 * q^24 - 221760 * q^26 + 196140 * q^29 - 303680 * q^31 + 917470 * q^34 - 56860 * q^36 - 1356320 * q^39 + 1247520 * q^41 - 1244130 * q^44 + 1715820 * q^46 - 3072730 * q^49 + 2870080 * q^51 + 5069810 * q^54 - 7534740 * q^56 + 779880 * q^59 + 3830220 * q^61 + 10766750 * q^64 - 14453830 * q^66 - 6847080 * q^69 + 1993920 * q^71 - 18672060 * q^74 + 12347570 * q^76 + 5708240 * q^79 - 14688950 * q^81 + 24299580 * q^84 + 37033080 * q^86 - 4090680 * q^89 - 11768320 * q^91 - 40784600 * q^94 + 24735710 * q^96 + 17045320 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(25, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.8.b.a	$25$	$8$	25.b	5.b	$2$	$2$	$2$	$7.810$	\(\Q(\sqrt{-1}) \)	None					5.8.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+7\beta q^{2}-24\beta q^{3}-68 q^{4}+672 q^{6}+\cdots\)
25.8.b.b	$25$	$8$	25.b	5.b	$2$	$4$	$4$	$7.810$	\(\Q(i, \sqrt{649})\)	None		✓			25.8.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+2\beta _{2})q^{2}+(2\beta _{1}-5\beta _{2})q^{3}+\cdots\)
25.8.b.c	$25$	$8$	25.b	5.b	$2$	$4$	$4$	$7.810$	\(\Q(i, \sqrt{19})\)	None					5.8.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{3})q^{2}+(-\beta _{1}+8\beta _{3})q^{3}+(-48+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(25, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)