Space of modular forms of level 425, weight 2, and Character 425.k

• Label: 425.2.k
• Level: $425$
• Weight: $2$
• Character orbit: 425.k
• Rep. character: $\chi_{425}(86,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $160$
• Newform subspaces: $3$
• Sturm bound: $90$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(90\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(425, [\chi])\).

	Total	New	Old
Modular forms	184	160	24
Cusp forms	168	160	8
Eisenstein series	16	0	16

Trace form

160 * q - 4 * q^3 - 40 * q^4 + 8 * q^5 - 4 * q^6 - 8 * q^7 + 18 * q^8 - 44 * q^9 - 18 * q^10 - 8 * q^11 + 8 * q^12 - 4 * q^13 - 20 * q^14 + 16 * q^15 - 16 * q^16 - 44 * q^18 + 6 * q^19 - 38 * q^20 + 6 * q^22 - 8 * q^23 + 20 * q^24 + 16 * q^25 - 20 * q^26 + 2 * q^27 + 24 * q^28 - 52 * q^30 - 12 * q^31 - 64 * q^32 - 16 * q^33 - 4 * q^34 - 36 * q^35 - 26 * q^36 - 24 * q^37 + 28 * q^38 - 12 * q^39 + 52 * q^40 + 2 * q^41 - 30 * q^42 - 12 * q^43 - 20 * q^44 + 74 * q^45 - 48 * q^46 - 28 * q^47 + 136 * q^49 + 10 * q^50 + 32 * q^51 + 82 * q^52 - 60 * q^53 - 40 * q^54 - 2 * q^55 - 24 * q^56 + 80 * q^57 + 40 * q^58 + 6 * q^59 + 80 * q^60 - 12 * q^61 + 14 * q^62 + 22 * q^63 - 22 * q^64 - 64 * q^65 - 48 * q^66 + 38 * q^67 - 14 * q^69 - 48 * q^70 - 24 * q^71 + 106 * q^72 - 36 * q^73 + 52 * q^74 - 20 * q^75 - 96 * q^76 - 20 * q^77 - 44 * q^78 - 60 * q^79 + 188 * q^80 - 2 * q^81 - 52 * q^82 - 100 * q^83 - 76 * q^84 - 2 * q^85 - 44 * q^86 - 72 * q^87 + 52 * q^88 + 10 * q^89 - 16 * q^90 - 28 * q^91 + 98 * q^92 - 80 * q^93 + 96 * q^94 + 88 * q^95 + 116 * q^96 + 66 * q^97 - 54 * q^98 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(425, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
425.2.k.a	$425$	$2$	425.k	25.d	$5$	$4$	$1$	$3.394$	\(\Q(\zeta_{10})\)	None		✓			425.2.k.a	$2$	$0$	\(4\)	\(1\)	\(-5\)	\(14\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(2-\zeta_{10}+\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+\cdots\)
425.2.k.b	$425$	$2$	425.k	25.d	$5$	$76$	$19$	$3.394$		None		✓			425.2.k.b	$2$	$0$	\(-6\)	\(-7\)	\(13\)	\(22\)		$\mathrm{SU}(2)[C_{5}]$
425.2.k.c	$425$	$2$	425.k	25.d	$5$	$80$	$20$	$3.394$		None		✓	✓		425.2.k.c	$2$	$0$	\(2\)	\(2\)	\(0\)	\(-44\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(425, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(425, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)