Space of modular forms of level 495, weight 2, and Character 495.c

• Label: 495.2.c
• Level: $495$
• Weight: $2$
• Character orbit: 495.c
• Rep. character: $\chi_{495}(199,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $5$
• Sturm bound: $144$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(144\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(495, [\chi])\).

	Total	New	Old
Modular forms	80	24	56
Cusp forms	64	24	40
Eisenstein series	16	0	16

Trace form

24 * q - 18 * q^4 - q^5 - 6 * q^10 + 4 * q^11 + 4 * q^14 + 10 * q^16 + 16 * q^19 + 8 * q^20 + 5 * q^25 + 24 * q^26 + 12 * q^29 - 30 * q^31 - 40 * q^34 - 18 * q^35 + 8 * q^40 - 12 * q^41 - 14 * q^44 + 56 * q^46 - 24 * q^49 + 10 * q^50 + 3 * q^55 - 36 * q^56 - 18 * q^59 - 4 * q^61 - 14 * q^64 - 40 * q^65 + 32 * q^70 + 54 * q^71 - 44 * q^74 - 40 * q^76 + 20 * q^79 + 46 * q^80 + 10 * q^85 + 28 * q^86 + 34 * q^89 - 12 * q^94 + 36 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(495, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
495.2.c.a	$495$	$2$	495.c	5.b	$2$	$4$	$4$	$3.953$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None					55.2.b.a	$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
495.2.c.b	$495$	$2$	495.c	5.b	$2$	$4$	$4$	$3.953$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		✓			495.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
495.2.c.c	$495$	$2$	495.c	5.b	$2$	$4$	$4$	$3.953$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		✓			495.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
495.2.c.d	$495$	$2$	495.c	5.b	$2$	$6$	$6$	$3.953$	6.0.350464.1	None					165.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{3}-\beta _{5})q^{2}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)
495.2.c.e	$495$	$2$	495.c	5.b	$2$	$6$	$6$	$3.953$	6.0.350464.1	None					165.2.c.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(495, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(495, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)