Space of modular forms of level 2646, weight 2, and Character 2646.h

• Label: 2646.2.h
• Level: $2646$
• Weight: $2$
• Character orbit: 2646.h
• Rep. character: $\chi_{2646}(361,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $20$
• Sturm bound: $1008$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.h (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(1008\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2646, [\chi])\).

	Total	New	Old
Modular forms	1104	80	1024
Cusp forms	912	80	832
Eisenstein series	192	0	192

Trace form

80 * q - 40 * q^4 + 8 * q^5 - 16 * q^11 - 2 * q^13 - 40 * q^16 - 14 * q^17 + 4 * q^19 - 4 * q^20 - 4 * q^23 + 80 * q^25 - 16 * q^26 - 18 * q^29 - 2 * q^31 - 2 * q^37 + 24 * q^38 - 6 * q^41 - 2 * q^43 + 8 * q^44 + 6 * q^46 - 6 * q^47 + 4 * q^52 + 32 * q^53 + 12 * q^55 + 12 * q^58 - 22 * q^59 - 8 * q^61 + 44 * q^62 + 80 * q^64 + 2 * q^65 - 14 * q^67 + 28 * q^68 + 76 * q^71 + 28 * q^73 + 12 * q^74 + 4 * q^76 - 32 * q^79 - 4 * q^80 + 16 * q^83 - 24 * q^85 - 40 * q^86 - 36 * q^89 + 2 * q^92 - 12 * q^94 + 42 * q^95 - 2 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(2646, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2646.2.h.a	$2646$	$2$	2646.h	63.g	$3$	$2$	$1$	$21.128$	\(\Q(\sqrt{-3}) \)	None					126.2.f.a	$2$	$0$	\(-1\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3q^{5}+q^{8}+\cdots\)
2646.2.h.b	$2646$	$2$	2646.h	63.g	$3$	$2$	$1$	$21.128$	\(\Q(\sqrt{-3}) \)	None					126.2.f.b	$2$	$0$	\(-1\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2q^{5}+q^{8}+\cdots\)
2646.2.h.c	$2646$	$2$	2646.h	63.g	$3$	$2$	$1$	$21.128$	\(\Q(\sqrt{-3}) \)	None					126.2.f.b	$2$	$0$	\(-1\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2q^{5}+q^{8}+\cdots\)
2646.2.h.d	$2646$	$2$	2646.h	63.g	$3$	$2$	$1$	$21.128$	\(\Q(\sqrt{-3}) \)	None					126.2.e.a	$2$	$0$	\(-1\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3q^{5}+q^{8}+\cdots\)
2646.2.h.e	$2646$	$2$	2646.h	63.g	$3$	$2$	$1$	$21.128$	\(\Q(\sqrt{-3}) \)	None					126.2.f.a	$2$	$0$	\(-1\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3q^{5}+q^{8}+\cdots\)
2646.2.h.f	$2646$	$2$	2646.h	63.g	$3$	$2$	$1$	$21.128$	\(\Q(\sqrt{-3}) \)	None					126.2.e.b	$2$	$0$	\(1\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3q^{5}-q^{8}+\cdots\)
2646.2.h.g	$2646$	$2$	2646.h	63.g	$3$	$2$	$1$	$21.128$	\(\Q(\sqrt{-3}) \)	None					882.2.f.b	$2$	$0$	\(1\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
2646.2.h.h	$2646$	$2$	2646.h	63.g	$3$	$2$	$1$	$21.128$	\(\Q(\sqrt{-3}) \)	None					18.2.c.a	$2$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{8}+3q^{11}+\cdots\)
2646.2.h.i	$2646$	$2$	2646.h	63.g	$3$	$2$	$1$	$21.128$	\(\Q(\sqrt{-3}) \)	None					18.2.c.a	$2$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{8}+3q^{11}+\cdots\)
2646.2.h.j	$2646$	$2$	2646.h	63.g	$3$	$2$	$1$	$21.128$	\(\Q(\sqrt{-3}) \)	None					882.2.f.b	$2$	$0$	\(1\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots\)
2646.2.h.k	$2646$	$2$	2646.h	63.g	$3$	$4$	$2$	$21.128$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None					126.2.f.d	$2$	$0$	\(-2\)	\(0\)	\(-6\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
2646.2.h.l	$2646$	$2$	2646.h	63.g	$3$	$4$	$2$	$21.128$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None					126.2.f.d	$2$	$0$	\(-2\)	\(0\)	\(6\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+(1-\beta _{2})q^{5}+\cdots\)
2646.2.h.m	$2646$	$2$	2646.h	63.g	$3$	$4$	$2$	$21.128$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					126.2.f.c	$2$	$0$	\(2\)	\(0\)	\(-4\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
2646.2.h.n	$2646$	$2$	2646.h	63.g	$3$	$4$	$2$	$21.128$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					126.2.f.c	$2$	$0$	\(2\)	\(0\)	\(4\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1})q^{2}-\beta _{1}q^{4}+(1-\beta _{3})q^{5}+\cdots\)
2646.2.h.o	$2646$	$2$	2646.h	63.g	$3$	$6$	$3$	$21.128$	6.0.309123.1	None					126.2.e.c	$2$	$0$	\(-3\)	\(0\)	\(-2\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{2}+(-1+\beta _{4})q^{4}+\beta _{3}q^{5}+q^{8}+\cdots\)
2646.2.h.p	$2646$	$2$	2646.h	63.g	$3$	$6$	$3$	$21.128$	6.0.309123.1	None					126.2.e.d	$2$	$0$	\(3\)	\(0\)	\(10\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{4})q^{2}-\beta _{4}q^{4}+(2+\beta _{1})q^{5}+\cdots\)
2646.2.h.q	$2646$	$2$	2646.h	63.g	$3$	$8$	$4$	$21.128$	\(\Q(\zeta_{24})\)	None					882.2.f.s	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta_1-1)q^{2}-\beta_1 q^{4}+(\beta_{6}+\beta_{5})q^{5}+\cdots\)
2646.2.h.r	$2646$	$2$	2646.h	63.g	$3$	$8$	$4$	$21.128$	\(\Q(\sqrt{-3}, \sqrt{-5}, \sqrt{7})\)	None					882.2.f.r	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(-\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)
2646.2.h.s	$2646$	$2$	2646.h	63.g	$3$	$8$	$4$	$21.128$	\(\Q(\sqrt{2}, \sqrt{-3}, \sqrt{-5})\)	None					882.2.f.p	$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{2}+(-1+\beta _{3})q^{4}-\beta _{1}q^{5}-q^{8}+\cdots\)
2646.2.h.t	$2646$	$2$	2646.h	63.g	$3$	$8$	$4$	$21.128$	\(\Q(\zeta_{24})\)	None					882.2.f.q	$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta_1+1)q^{2}-\beta_1 q^{4}+(-2\beta_{6}-2\beta_{5})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2646, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2646, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)