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

\( 90 q + 2 q^{2} + 94 q^{4} + 6 q^{8} - 98 q^{9} + O(q^{10}) \)

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	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		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-2iq^{3}-q^{4}+iq^{5}+2iq^{6}+\cdots\)
1445.2.d.b	$1445$	$2$	1445.d	17.b	$2$	$2$	$2$	$11.538$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+iq^{3}-q^{4}+iq^{5}-iq^{6}-5iq^{7}+\cdots\)
1445.2.d.c	$1445$	$2$	1445.d	17.b	$2$	$2$	$2$	$11.538$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{3}-2q^{4}+iq^{5}-2iq^{7}-q^{9}+\cdots\)
1445.2.d.d	$1445$	$2$	1445.d	17.b	$2$	$4$	$4$	$11.538$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{3})q^{2}-\beta _{1}q^{3}+(3-\beta _{3})q^{4}+\cdots\)
1445.2.d.e	$1445$	$2$	1445.d	17.b	$2$	$4$	$4$	$11.538$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{3}q^{2}+(-\zeta_{12}+\zeta_{12}^{2})q^{3}+q^{4}+\cdots\)
1445.2.d.f	$1445$	$2$	1445.d	17.b	$2$	$4$	$4$	$11.538$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{8}^{3})q^{2}+(-2\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots\)
1445.2.d.g	$1445$	$2$	1445.d	17.b	$2$	$12$	$12$	$11.538$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+(-\beta _{1}-\beta _{7})q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)
1445.2.d.h	$1445$	$2$	1445.d	17.b	$2$	$12$	$12$	$11.538$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(6\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{8})q^{2}+(\beta _{1}-\beta _{9})q^{3}+(1-\beta _{7}+\cdots)q^{4}+\cdots\)
1445.2.d.i	$1445$	$2$	1445.d	17.b	$2$	$24$	$24$	$11.538$		None		$2$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1445.2.d.j	$1445$	$2$	1445.d	17.b	$2$	$24$	$24$	$11.538$		None		$2$	$0$	\(8\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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