Space of modular forms of level 1445, weight 2, and Character 1445.d

• Label: 1445.2.d
• Level: $1445$
• Weight: $2$
• Character orbit: 1445.d
• Rep. character: $\chi_{1445}(866,\cdot)$
• Character field: $\Q$
• Dimension: $90$
• Newform subspaces: $10$
• Sturm bound: $306$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(306\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1445, [\chi])\).

	Total	New	Old
Modular forms	170	90	80
Cusp forms	134	90	44
Eisenstein series	36	0	36

Trace form

90 * q + 2 * q^2 + 94 * q^4 + 6 * q^8 - 98 * q^9 - 8 * q^13 + 102 * q^16 + 2 * q^18 - 90 * q^25 + 28 * q^26 - 4 * q^30 - 6 * q^32 - 12 * q^33 - 4 * q^35 - 118 * q^36 - 8 * q^38 - 12 * q^42 - 28 * q^43 + 16 * q^47 - 78 * q^49 - 2 * q^50 + 40 * q^53 - 8 * q^55 - 4 * q^59 - 12 * q^60 + 106 * q^64 + 12 * q^66 - 16 * q^67 - 24 * q^69 + 36 * q^70 - 10 * q^72 - 12 * q^76 + 56 * q^77 + 106 * q^81 + 4 * q^83 - 36 * q^84 - 12 * q^86 - 24 * q^87 - 12 * q^89 + 68 * q^93 + 8 * q^94 - 94 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1445, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1445.2.d.a	$1445$	$2$	1445.d	17.b	$2$	$2$	$2$	$11.538$	\(\Q(\sqrt{-1}) \)	None					85.2.a.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-2 i q^{3}-q^{4}+i q^{5}+2 i q^{6}+\cdots\)
1445.2.d.b	$1445$	$2$	1445.d	17.b	$2$	$2$	$2$	$11.538$	\(\Q(\sqrt{-1}) \)	None		✓			1445.2.a.d	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+i q^{3}-q^{4}+i q^{5}-i q^{6}+\cdots\)
1445.2.d.c	$1445$	$2$	1445.d	17.b	$2$	$2$	$2$	$11.538$	\(\Q(\sqrt{-1}) \)	None		✓			1445.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 i q^{3}-2 q^{4}+i q^{5}-2 i q^{7}+\cdots\)
1445.2.d.d	$1445$	$2$	1445.d	17.b	$2$	$4$	$4$	$11.538$	\(\Q(i, \sqrt{17})\)	None		✓			1445.2.a.h	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{3})q^{2}-\beta _{1}q^{3}+(3-\beta _{3})q^{4}+\cdots\)
1445.2.d.e	$1445$	$2$	1445.d	17.b	$2$	$4$	$4$	$11.538$	\(\Q(\zeta_{12})\)	None					85.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{3} q^{2}+(\beta_{2}-\beta_1)q^{3}+q^{4}-\beta_1 q^{5}+\cdots\)
1445.2.d.f	$1445$	$2$	1445.d	17.b	$2$	$4$	$4$	$11.538$	\(\Q(\zeta_{8})\)	None					85.2.a.b	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{3}+1)q^{2}+(\beta_{2}-2\beta_1)q^{3}+(2\beta_{3}+1)q^{4}+\cdots\)
1445.2.d.g	$1445$	$2$	1445.d	17.b	$2$	$12$	$12$	$11.538$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					85.2.e.a	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+(-\beta _{1}-\beta _{7})q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)
1445.2.d.h	$1445$	$2$	1445.d	17.b	$2$	$12$	$12$	$11.538$	12.0.\(\cdots\).1	None		✓			1445.2.a.l	$2$	$0$	\(6\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{8})q^{2}+(\beta _{1}-\beta _{9})q^{3}+(1-\beta _{7}+\cdots)q^{4}+\cdots\)
1445.2.d.i	$1445$	$2$	1445.d	17.b	$2$	$24$	$24$	$11.538$		None		✓			1445.2.a.r	$2$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1445.2.d.j	$1445$	$2$	1445.d	17.b	$2$	$24$	$24$	$11.538$		None					85.2.l.a	$2$	$0$	\(8\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1445, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1445, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 2}\)