Space of modular forms of level 845, weight 2, and Character 845.b

• Label: 845.2.b
• Level: $845$
• Weight: $2$
• Character orbit: 845.b
• Rep. character: $\chi_{845}(339,\cdot)$
• Character field: $\Q$
• Dimension: $66$
• Newform subspaces: $8$
• Sturm bound: $182$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(182\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(845, [\chi])\).

	Total	New	Old
Modular forms	106	88	18
Cusp forms	78	66	12
Eisenstein series	28	22	6

Trace form

66 * q - 50 * q^4 - 4 * q^6 - 42 * q^9 + 2 * q^10 + 12 * q^11 - 32 * q^14 - 16 * q^15 + 18 * q^16 + 20 * q^20 + 4 * q^21 - 16 * q^24 - 4 * q^25 + 16 * q^29 + 26 * q^30 + 20 * q^31 - 20 * q^34 - 4 * q^35 + 34 * q^36 + 18 * q^40 + 8 * q^41 - 40 * q^44 + 4 * q^45 - 32 * q^46 - 22 * q^49 - 16 * q^50 - 32 * q^51 + 68 * q^54 + 8 * q^55 + 8 * q^56 - 16 * q^59 + 12 * q^60 - 8 * q^61 + 94 * q^64 - 8 * q^66 + 12 * q^69 + 20 * q^70 + 24 * q^71 - 12 * q^74 - 10 * q^75 + 20 * q^76 - 56 * q^79 - 48 * q^80 - 78 * q^81 - 12 * q^84 + 12 * q^85 + 32 * q^86 + 20 * q^89 - 20 * q^90 + 64 * q^94 - 2 * q^95 + 36 * q^96 - 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(845, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
845.2.b.a	$845$	$2$	845.b	5.b	$2$	$2$	$2$	$6.747$	\(\Q(\sqrt{-1}) \)	None					65.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-2 i q^{3}+q^{4}+(i-2)q^{5}+\cdots\)
845.2.b.b	$845$	$2$	845.b	5.b	$2$	$2$	$2$	$6.747$	\(\Q(\sqrt{-1}) \)	None					65.2.d.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+2 i q^{3}+q^{4}+(i+2)q^{5}+\cdots\)
845.2.b.c	$845$	$2$	845.b	5.b	$2$	$6$	$6$	$6.747$	6.0.350464.1	None					65.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{5})q^{2}+(\beta _{3}+\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots\)
845.2.b.d	$845$	$2$	845.b	5.b	$2$	$6$	$6$	$6.747$	6.0.49843600.1	None					65.2.n.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.b.e	$845$	$2$	845.b	5.b	$2$	$6$	$6$	$6.747$	6.0.49843600.1	None					65.2.n.a	$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.b.f	$845$	$2$	845.b	5.b	$2$	$8$	$8$	$6.747$	8.0.49787136.1	None					65.2.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+\beta _{3}q^{3}+\beta _{4}q^{4}+(-\beta _{2}-\beta _{7})q^{5}+\cdots\)
845.2.b.g	$845$	$2$	845.b	5.b	$2$	$18$	$18$	$6.747$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		✓			845.2.b.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{15}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
845.2.b.h	$845$	$2$	845.b	5.b	$2$	$18$	$18$	$6.747$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		✓			845.2.b.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{15}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(845, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(845, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)