Space of modular forms of level 25, weight 2, and Character 25.e

• Label: 25.2.e
• Level: $25$
• Weight: $2$
• Character orbit: 25.e
• Rep. character: $\chi_{25}(4,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $5$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	25.e (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(5\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(25, [\chi])\).

	Total	New	Old
Modular forms	16	16	0
Cusp forms	8	8	0
Eisenstein series	8	8	0

Trace form

8 * q - 5 * q^2 - 5 * q^3 - q^4 - 9 * q^6 + 10 * q^8 + q^9 - 5 * q^10 - 4 * q^11 + 15 * q^12 - 5 * q^13 + 13 * q^14 + 15 * q^15 + 3 * q^16 - 10 * q^17 - 5 * q^19 - 15 * q^20 - 4 * q^21 + 5 * q^23 - 20 * q^24 - 10 * q^25 + 6 * q^26 - 5 * q^27 - 15 * q^28 - 5 * q^29 + 15 * q^30 - 9 * q^31 + 10 * q^33 + 13 * q^34 + 15 * q^35 + 23 * q^36 + 30 * q^37 + 15 * q^38 - 3 * q^39 + 10 * q^40 - 4 * q^41 - 15 * q^42 - 2 * q^44 - 15 * q^45 - 19 * q^46 - 30 * q^48 + 14 * q^49 - 15 * q^50 - 4 * q^51 - 10 * q^52 - 10 * q^53 - 5 * q^54 - 10 * q^55 + 10 * q^56 + 20 * q^58 - 10 * q^60 - 9 * q^61 - 30 * q^62 + 10 * q^63 + 4 * q^64 + 5 * q^65 + 12 * q^66 + 20 * q^67 + 17 * q^69 + 30 * q^70 + 6 * q^71 + 5 * q^72 + 15 * q^73 - 12 * q^74 - 10 * q^75 - 20 * q^76 + 10 * q^77 + 25 * q^78 + 15 * q^79 + 20 * q^80 + 28 * q^81 - 45 * q^83 + 18 * q^84 - 15 * q^85 - 9 * q^86 - 20 * q^87 - 20 * q^88 - 25 * q^89 - 25 * q^90 + 6 * q^91 + 30 * q^92 - 27 * q^94 + 15 * q^95 + 16 * q^96 - 60 * q^97 - 10 * q^98 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(25, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.2.e.a	$25$	$2$	25.e	25.e	$10$	$8$	$2$	$0.200$	8.0.58140625.2	None		✓	✓	✓	25.2.e.a	$2$	$0$	\(-5\)	\(-5\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-1+\beta _{1})q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{7})q^{3}+\cdots\)