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

• Label: 845.2.e
• Level: $845$
• Weight: $2$
• Character orbit: 845.e
• Rep. character: $\chi_{845}(146,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $104$
• Newform subspaces: $16$
• Sturm bound: $182$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(182\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	208	104	104
Cusp forms	152	104	48
Eisenstein series	56	0	56

Trace form

104 * q + 2 * q^3 - 54 * q^4 - 6 * q^6 + 2 * q^7 + 12 * q^8 - 56 * q^9 + 2 * q^10 + 4 * q^12 - 4 * q^14 - 2 * q^15 - 62 * q^16 + 14 * q^17 - 8 * q^18 - 4 * q^20 - 16 * q^21 + 6 * q^23 + 4 * q^24 + 104 * q^25 + 20 * q^27 - 10 * q^28 - 4 * q^30 + 16 * q^31 - 2 * q^32 - 14 * q^33 + 12 * q^34 + 6 * q^35 - 44 * q^36 + 6 * q^37 - 72 * q^38 - 12 * q^40 + 12 * q^41 + 16 * q^42 - 14 * q^43 - 20 * q^44 + 8 * q^45 + 14 * q^46 - 24 * q^47 + 32 * q^48 - 56 * q^49 + 16 * q^51 - 64 * q^53 + 10 * q^54 + 12 * q^55 + 48 * q^56 - 12 * q^57 + 32 * q^58 + 12 * q^59 + 16 * q^60 + 16 * q^61 + 20 * q^62 + 12 * q^63 + 88 * q^64 - 4 * q^66 - 6 * q^67 + 58 * q^68 - 4 * q^69 + 8 * q^70 - 20 * q^71 + 12 * q^72 + 56 * q^73 + 10 * q^74 + 2 * q^75 - 26 * q^76 - 36 * q^77 - 16 * q^79 - 68 * q^81 + 8 * q^83 - 18 * q^84 - 6 * q^85 - 60 * q^86 - 10 * q^87 + 14 * q^88 - 16 * q^89 - 16 * q^90 - 44 * q^92 - 8 * q^93 + 8 * q^94 + 8 * q^95 - 4 * q^96 - 22 * q^97 - 12 * q^98 - 32 * 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.e.a	$845$	$2$	845.e	13.c	$3$	$2$	$1$	$6.747$	\(\Q(\sqrt{-3}) \)	None					65.2.a.a	$2$	$0$	\(-1\)	\(2\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
845.2.e.b	$845$	$2$	845.e	13.c	$3$	$2$	$1$	$6.747$	\(\Q(\sqrt{-3}) \)	None					65.2.a.a	$2$	$0$	\(1\)	\(2\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
845.2.e.c	$845$	$2$	845.e	13.c	$3$	$4$	$2$	$6.747$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					65.2.a.b	$2$	$0$	\(-2\)	\(0\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
845.2.e.d	$845$	$2$	845.e	13.c	$3$	$4$	$2$	$6.747$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None					65.2.e.b	$2$	$0$	\(-1\)	\(-2\)	\(4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
845.2.e.e	$845$	$2$	845.e	13.c	$3$	$4$	$2$	$6.747$	\(\Q(\zeta_{12})\)	None					65.2.a.c	$2$	$0$	\(0\)	\(-2\)	\(-4\)	\(-4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta_{2} q^{2}+(\beta_{2}-\beta_1)q^{3}+(\beta_1-1)q^{4}+\cdots\)
845.2.e.f	$845$	$2$	845.e	13.c	$3$	$4$	$2$	$6.747$	\(\Q(\zeta_{12})\)	None					65.2.a.c	$2$	$0$	\(0\)	\(-2\)	\(4\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta_{2} q^{2}+(-\beta_{2}-\beta_1)q^{3}+(\beta_1-1)q^{4}+\cdots\)
845.2.e.g	$845$	$2$	845.e	13.c	$3$	$4$	$2$	$6.747$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None					65.2.e.a	$2$	$0$	\(1\)	\(0\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-1+2\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
845.2.e.h	$845$	$2$	845.e	13.c	$3$	$4$	$2$	$6.747$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					65.2.a.b	$2$	$0$	\(2\)	\(0\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{1}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.e.i	$845$	$2$	845.e	13.c	$3$	$6$	$3$	$6.747$	6.0.954288.1	None					65.2.c.a	$2$	$0$	\(-1\)	\(2\)	\(-6\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{4}-\beta _{5})q^{2}+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
845.2.e.j	$845$	$2$	845.e	13.c	$3$	$6$	$3$	$6.747$	6.0.64827.1	None		✓			845.2.a.h	$2$	$0$	\(-1\)	\(5\)	\(-6\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(2-\beta _{4}-2\beta _{5})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.e.k	$845$	$2$	845.e	13.c	$3$	$6$	$3$	$6.747$	6.0.954288.1	None					65.2.c.a	$2$	$0$	\(1\)	\(2\)	\(6\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{4}+\beta _{5})q^{2}+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
845.2.e.l	$845$	$2$	845.e	13.c	$3$	$6$	$3$	$6.747$	6.0.64827.1	None		✓			845.2.a.h	$2$	$0$	\(1\)	\(5\)	\(6\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(2-\beta _{4}-2\beta _{5})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.e.m	$845$	$2$	845.e	13.c	$3$	$8$	$4$	$6.747$	8.0.22581504.2	None					65.2.m.a	$2$	$0$	\(-2\)	\(2\)	\(-8\)	\(-10\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}+\beta _{5})q^{2}+(\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
845.2.e.n	$845$	$2$	845.e	13.c	$3$	$8$	$4$	$6.747$	8.0.22581504.2	None					65.2.m.a	$2$	$0$	\(2\)	\(2\)	\(8\)	\(10\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1}-\beta _{5})q^{2}+(\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
845.2.e.o	$845$	$2$	845.e	13.c	$3$	$18$	$9$	$6.747$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		✓			845.2.a.n	$2$	$0$	\(-3\)	\(-7\)	\(18\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{3}-\beta _{5}+\beta _{6}-\beta _{7}+\beta _{10}+\cdots)q^{2}+\cdots\)
845.2.e.p	$845$	$2$	845.e	13.c	$3$	$18$	$9$	$6.747$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		✓			845.2.a.n	$2$	$0$	\(3\)	\(-7\)	\(-18\)	\(7\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{3}+\beta _{5}-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{2}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(845, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)