Space of modular forms of level 645, weight 2, and Character 645.s

• Label: 645.2.s
• Level: $645$
• Weight: $2$
• Character orbit: 645.s
• Rep. character: $\chi_{645}(566,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $116$
• Newform subspaces: $4$
• Sturm bound: $176$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 645 = 3 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	645.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 129 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(176\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(645, [\chi])\).

	Total	New	Old
Modular forms	184	116	68
Cusp forms	168	116	52
Eisenstein series	16	0	16

Trace form

116 * q + 112 * q^4 + 2 * q^6 + 6 * q^7 - 10 * q^9 - 10 * q^13 + 136 * q^16 - 24 * q^19 - 8 * q^21 + 6 * q^24 - 58 * q^25 - 36 * q^28 - 6 * q^30 - 18 * q^31 + 60 * q^33 - 22 * q^36 - 6 * q^37 - 40 * q^43 - 36 * q^46 + 28 * q^49 - 28 * q^52 - 44 * q^54 + 2 * q^57 - 32 * q^58 + 14 * q^60 - 60 * q^61 - 30 * q^63 + 152 * q^64 - 8 * q^66 + 38 * q^67 + 24 * q^69 - 162 * q^72 + 150 * q^73 - 60 * q^76 - 256 * q^78 - 40 * q^79 - 2 * q^81 - 4 * q^84 + 56 * q^87 - 88 * q^90 - 30 * q^91 + 6 * q^93 + 18 * q^96 + 184 * q^97 - 10 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(645, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
645.2.s.a	$645$	$2$	645.s	129.h	$6$	$4$	$2$	$5.150$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		✓			645.2.s.a	$2$	$1$	\(-4\)	\(-2\)	\(-2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-q^{2}+(-\beta _{1}+\beta _{3})q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots\)
645.2.s.b	$645$	$2$	645.s	129.h	$6$	$4$	$2$	$5.150$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		✓			645.2.s.a	$2$	$0$	\(4\)	\(-1\)	\(2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+q^{2}-\beta _{1}q^{3}-q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
645.2.s.c	$645$	$2$	645.s	129.h	$6$	$54$	$27$	$5.150$		None		✓			645.2.s.c	$2$	$0$	\(-4\)	\(1\)	\(27\)	\(6\)		$\mathrm{SU}(2)[C_{6}]$
645.2.s.d	$645$	$2$	645.s	129.h	$6$	$54$	$27$	$5.150$		None		✓			645.2.s.c	$2$	$0$	\(4\)	\(2\)	\(-27\)	\(6\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(645, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(645, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(129, [\chi])\)\(^{\oplus 2}\)