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

• Label: 1445.2.b
• Level: $1445$
• Weight: $2$
• Character orbit: 1445.b
• Rep. character: $\chi_{1445}(579,\cdot)$
• Character field: $\Q$
• Dimension: $120$
• Newform subspaces: $9$
• Sturm bound: $306$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(306\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	172	150	22
Cusp forms	136	120	16
Eisenstein series	36	30	6

Trace form

120 * q - 104 * q^4 + 2 * q^5 - 88 * q^9 - 6 * q^10 + 4 * q^11 - 12 * q^14 - 2 * q^15 + 88 * q^16 + 12 * q^19 + 2 * q^20 - 24 * q^21 - 12 * q^24 + 10 * q^25 - 8 * q^29 + 26 * q^30 + 24 * q^31 - 20 * q^35 + 28 * q^36 - 44 * q^39 - 22 * q^40 + 12 * q^41 + 32 * q^44 + 22 * q^45 + 8 * q^46 - 16 * q^49 - 38 * q^50 + 20 * q^54 + 14 * q^55 + 8 * q^56 - 8 * q^59 + 66 * q^60 - 12 * q^61 - 76 * q^64 - 20 * q^65 - 12 * q^66 - 20 * q^69 - 44 * q^70 + 20 * q^71 + 40 * q^74 - 4 * q^75 + 20 * q^76 - 24 * q^79 + 26 * q^80 + 8 * q^81 - 68 * q^84 - 88 * q^86 + 44 * q^89 + 74 * q^90 - 36 * q^91 - 16 * q^94 - 4 * q^95 - 16 * q^96 - 24 * q^99

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.b.a	$1445$	$2$	1445.b	5.b	$2$	$4$	$4$	$11.538$	\(\Q(\zeta_{8})\)	None					85.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{3})q^{3}+q^{4}+(-2\zeta_{8}+\cdots)q^{5}+\cdots\)
1445.2.b.b	$1445$	$2$	1445.b	5.b	$2$	$8$	$8$	$11.538$	8.0.\(\cdots\).11	None					85.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-\beta _{3}q^{3}+(-2-\beta _{4})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots\)
1445.2.b.c	$1445$	$2$	1445.b	5.b	$2$	$8$	$8$	$11.538$	8.0.\(\cdots\).1	None		✓			1445.2.b.c	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{6}q^{3}+(-1+\beta _{1})q^{4}+\beta _{2}q^{5}+\cdots\)
1445.2.b.d	$1445$	$2$	1445.b	5.b	$2$	$8$	$8$	$11.538$	8.0.\(\cdots\).1	None		✓			1445.2.b.c	$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-\beta _{6}q^{3}+(-1+\beta _{1})q^{4}-\beta _{2}q^{5}+\cdots\)
1445.2.b.e	$1445$	$2$	1445.b	5.b	$2$	$8$	$8$	$11.538$	8.0.619810816.2	None					85.2.b.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}+(-\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{3}+\cdots\)
1445.2.b.f	$1445$	$2$	1445.b	5.b	$2$	$12$	$12$	$11.538$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					85.2.j.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-\beta _{10}q^{3}+(-1+\beta _{8})q^{4}+\cdots\)
1445.2.b.g	$1445$	$2$	1445.b	5.b	$2$	$24$	$24$	$11.538$		None		✓			1445.2.b.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1445.2.b.h	$1445$	$2$	1445.b	5.b	$2$	$24$	$24$	$11.538$		None		✓			1445.2.b.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1445.2.b.i	$1445$	$2$	1445.b	5.b	$2$	$24$	$24$	$11.538$		None					85.2.m.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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