Space of modular forms of level 425, weight 4, and Character 425.d

• Label: 425.4.d
• Level: $425$
• Weight: $4$
• Character orbit: 425.d
• Rep. character: $\chi_{425}(101,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $8$
• Sturm bound: $180$
• Trace bound: $8$

Defining parameters

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	425.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(180\)
Trace bound:			\(8\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(425, [\chi])\).

	Total	New	Old
Modular forms	142	88	54
Cusp forms	130	82	48
Eisenstein series	12	6	6

Trace form

82 * q - 2 * q^2 + 326 * q^4 - 30 * q^8 - 602 * q^9 - 72 * q^13 + 1414 * q^16 + 54 * q^17 + 326 * q^18 - 28 * q^19 - 332 * q^21 + 544 * q^26 + 798 * q^32 - 948 * q^33 - 428 * q^34 - 2118 * q^36 + 952 * q^38 - 1732 * q^42 + 68 * q^43 - 292 * q^47 - 4030 * q^49 + 1346 * q^51 - 1592 * q^52 - 380 * q^53 + 2416 * q^59 + 6062 * q^64 + 3876 * q^66 + 2372 * q^67 - 2610 * q^68 + 1652 * q^69 + 5642 * q^72 - 3564 * q^76 - 4716 * q^77 - 266 * q^81 - 1916 * q^83 - 7388 * q^84 + 4920 * q^86 - 520 * q^87 + 1252 * q^89 + 2508 * q^93 + 2168 * q^94 + 3870 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(425, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
425.4.d.a	$425$	$4$	425.d	17.b	$2$	$2$	$2$	$25.076$	\(\Q(\sqrt{-1}) \)	None					85.4.d.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-4\beta q^{3}-7 q^{4}+4\beta q^{6}+7\beta q^{7}+\cdots\)
425.4.d.b	$425$	$4$	425.d	17.b	$2$	$4$	$4$	$25.076$	\(\Q(\sqrt{-19}, \sqrt{-1131})\)	None		✓			425.4.d.b	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{2}q^{3}-7q^{4}+\beta _{2}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
425.4.d.c	$425$	$4$	425.d	17.b	$2$	$4$	$4$	$25.076$	\(\Q(\sqrt{-37 +3 \sqrt{33}})\)	None					17.4.b.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\cdots\)
425.4.d.d	$425$	$4$	425.d	17.b	$2$	$4$	$4$	$25.076$	\(\Q(\sqrt{-19}, \sqrt{-1131})\)	None		✓			425.4.d.b	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\beta _{2}q^{3}-7q^{4}-\beta _{2}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
425.4.d.e	$425$	$4$	425.d	17.b	$2$	$14$	$14$	$25.076$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			425.4.d.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(8-\beta _{3})q^{4}+\beta _{10}q^{6}+\cdots\)
425.4.d.f	$425$	$4$	425.d	17.b	$2$	$14$	$14$	$25.076$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			425.4.d.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(8-\beta _{3})q^{4}+\beta _{10}q^{6}+\cdots\)
425.4.d.g	$425$	$4$	425.d	17.b	$2$	$16$	$16$	$25.076$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					85.4.d.b	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{11}q^{3}+(6-\beta _{1})q^{4}+(-\beta _{8}+\cdots)q^{6}+\cdots\)
425.4.d.h	$425$	$4$	425.d	17.b	$2$	$24$	$24$	$25.076$		None			✓		85.4.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(425, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(425, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)