Space of modular forms of level 25, weight 4, and Character 25.b

• Label: 25.4.b
• Level: $25$
• Weight: $4$
• Character orbit: 25.b
• Rep. character: $\chi_{25}(24,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $10$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(10\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(25, [\chi])\).

	Total	New	Old
Modular forms	10	6	4
Cusp forms	4	4	0
Eisenstein series	6	2	4

Trace form

4 * q - 2 * q^4 - 2 * q^6 + 2 * q^9 - 22 * q^11 + 36 * q^14 - 46 * q^16 - 130 * q^19 + 108 * q^21 + 210 * q^24 + 248 * q^26 - 220 * q^29 - 132 * q^31 + 26 * q^34 - 676 * q^36 + 544 * q^39 - 362 * q^41 - 1114 * q^44 + 948 * q^46 + 1228 * q^49 + 1378 * q^51 - 730 * q^54 - 180 * q^56 - 440 * q^59 - 2072 * q^61 + 1358 * q^64 - 1114 * q^66 - 1956 * q^69 + 1648 * q^71 + 2756 * q^74 + 2090 * q^76 - 2220 * q^79 - 836 * q^81 + 396 * q^84 - 3352 * q^86 + 2190 * q^89 - 792 * q^91 - 4504 * q^94 + 3278 * q^96 + 3364 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(25, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.4.b.a	$25$	$4$	25.b	5.b	$2$	$2$	$2$	$1.475$	\(\Q(\sqrt{-1}) \)	None					5.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{2}+\beta q^{3}-8 q^{4}-8 q^{6}-3\beta q^{7}+\cdots\)
25.4.b.b	$25$	$4$	25.b	5.b	$2$	$2$	$2$	$1.475$	\(\Q(\sqrt{-1}) \)	None		✓			25.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-7 i q^{3}+7 q^{4}+7 q^{6}+6 i q^{7}+\cdots\)