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

• Label: 425.2.n
• Level: $425$
• Weight: $2$
• Character orbit: 425.n
• Rep. character: $\chi_{425}(49,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $104$
• Newform subspaces: $6$
• Sturm bound: $90$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.n (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(90\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	200	120	80
Cusp forms	152	104	48
Eisenstein series	48	16	32

Trace form

104 * q - 24 * q^6 + 8 * q^9 - 16 * q^11 + 40 * q^14 - 120 * q^16 + 40 * q^19 - 40 * q^24 + 56 * q^26 + 16 * q^29 + 24 * q^31 - 24 * q^34 + 72 * q^36 - 32 * q^39 - 16 * q^41 - 120 * q^44 - 24 * q^46 - 64 * q^49 - 24 * q^51 + 120 * q^54 + 24 * q^56 - 32 * q^59 - 64 * q^61 + 64 * q^66 - 32 * q^69 - 56 * q^71 + 24 * q^74 + 104 * q^76 + 104 * q^79 + 144 * q^84 - 48 * q^86 + 16 * q^94 - 112 * q^96 + 184 * 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.n.a	$425$	$2$	425.n	85.m	$8$	$4$	$1$	$3.394$	\(\Q(\zeta_{8})\)	None					17.2.d.a	$2$	$1$	\(-4\)	\(-4\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-1+\zeta_{8}-\zeta_{8}^{2})q^{2}+(-1+\zeta_{8}+\cdots)q^{3}+\cdots\)
425.2.n.b	$425$	$2$	425.n	85.m	$8$	$4$	$1$	$3.394$	\(\Q(\zeta_{8})\)	None					17.2.d.a	$2$	$0$	\(4\)	\(4\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(1-\zeta_{8}+\zeta_{8}^{2})q^{2}+(1-\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
425.2.n.c	$425$	$2$	425.n	85.m	$8$	$24$	$6$	$3.394$		None					85.2.l.a	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
425.2.n.d	$425$	$2$	425.n	85.m	$8$	$24$	$6$	$3.394$		None		✓			425.2.m.c	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
425.2.n.e	$425$	$2$	425.n	85.m	$8$	$24$	$6$	$3.394$		None		✓			425.2.m.c	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
425.2.n.f	$425$	$2$	425.n	85.m	$8$	$24$	$6$	$3.394$		None					85.2.l.a	$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

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

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