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

• Label: 425.2.d
• Level: $425$
• Weight: $2$
• Character orbit: 425.d
• Rep. character: $\chi_{425}(101,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $4$
• Sturm bound: $90$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(90\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

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

	Total	New	Old
Modular forms	50	32	18
Cusp forms	38	26	12
Eisenstein series	12	6	6

Trace form

26 * q + 2 * q^2 + 22 * q^4 + 6 * q^8 - 30 * q^9 - 8 * q^13 + 6 * q^16 + 2 * q^17 + 10 * q^18 + 8 * q^19 - 4 * q^21 - 6 * q^32 - 4 * q^33 + 10 * q^34 - 74 * q^36 - 8 * q^38 - 20 * q^42 - 28 * q^43 + 20 * q^47 + 10 * q^49 - 40 * q^51 + 28 * q^53 - 48 * q^59 - 18 * q^64 + 64 * q^66 - 12 * q^67 + 34 * q^68 + 40 * q^69 + 14 * q^72 - 80 * q^76 + 28 * q^77 + 26 * q^81 - 4 * q^83 + 60 * q^84 + 24 * q^86 - 32 * q^87 + 12 * q^89 + 36 * q^93 + 32 * q^94 - 86 * q^98

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.d.a	$425$	$2$	425.d	17.b	$2$	$6$	$6$	$3.394$	6.0.93924352.2	None		✓			425.2.d.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-\beta _{2}+\beta _{3})q^{4}+\cdots\)
425.2.d.b	$425$	$2$	425.d	17.b	$2$	$6$	$6$	$3.394$	6.0.93924352.2	None		✓			425.2.d.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-\beta _{2}+\beta _{3})q^{4}+\cdots\)
425.2.d.c	$425$	$2$	425.d	17.b	$2$	$6$	$6$	$3.394$	6.0.350464.1	None					85.2.d.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-\beta _{4}q^{3}+(\beta _{1}+\beta _{3})q^{4}-\beta _{5}q^{6}+\cdots\)
425.2.d.d	$425$	$2$	425.d	17.b	$2$	$8$	$8$	$3.394$	8.0.\(\cdots\).3	None			✓		85.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(2-\beta _{3})q^{4}+(\beta _{5}+\cdots)q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(425, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)