Space of modular forms of level 495, weight 2, and trivial character

• Label: 495.2.a
• Level: $495$
• Weight: $2$
• Character orbit: 495.a
• Rep. character: $\chi_{495}(1,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $7$
• Sturm bound: $144$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(144\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(495))\).

	Total	New	Old
Modular forms	80	18	62
Cusp forms	65	18	47
Eisenstein series	15	0	15

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	\(5\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(-\)	\(-\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(4\)
Plus space			\(+\)	\(3\)
Minus space			\(-\)	\(15\)

Trace form

18 * q + 26 * q^4 + 2 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^10 + 12 * q^13 + 20 * q^14 + 38 * q^16 - 4 * q^17 + 8 * q^19 + 2 * q^20 - 2 * q^22 + 4 * q^23 + 18 * q^25 - 16 * q^26 - 12 * q^28 + 4 * q^29 - 8 * q^31 + 24 * q^32 - 4 * q^35 + 20 * q^37 - 4 * q^41 + 12 * q^43 - 4 * q^44 - 28 * q^46 + 28 * q^47 + 42 * q^49 - 12 * q^52 + 12 * q^53 - 4 * q^55 + 12 * q^56 - 48 * q^58 - 4 * q^61 - 32 * q^62 - 6 * q^64 - 4 * q^65 + 4 * q^67 - 68 * q^68 - 20 * q^70 - 32 * q^71 + 12 * q^73 + 24 * q^74 - 40 * q^76 + 4 * q^77 + 32 * q^79 - 10 * q^80 - 64 * q^82 + 12 * q^83 + 12 * q^85 - 28 * q^86 - 6 * q^88 + 20 * q^89 - 32 * q^91 + 12 * q^92 - 68 * q^94 - 8 * q^95 + 36 * q^97 - 48 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(495))\) 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					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5	11
495.2.a.a	$495$	$2$	495.a	1.a	$1$	$1$	$1$	$3.953$	\(\Q\)	None	✓		✓	✓	55.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}+q^{11}+\cdots\)
495.2.a.b	$495$	$2$	495.a	1.a	$1$	$2$	$2$	$3.953$	\(\Q(\sqrt{2}) \)	None	✓		✓	✓	55.2.a.b	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}-2q^{7}+\cdots\)
495.2.a.c	$495$	$2$	495.a	1.a	$1$	$2$	$2$	$3.953$	\(\Q(\sqrt{3}) \)	None	✓				165.2.a.b	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+q^{5}+2q^{7}-\beta q^{8}+\beta q^{10}+\cdots\)
495.2.a.d	$495$	$2$	495.a	1.a	$1$	$2$	$2$	$3.953$	\(\Q(\sqrt{2}) \)	None	✓				165.2.a.a	$1$	$0$	\(2\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}+(-2+\cdots)q^{7}+\cdots\)
495.2.a.e	$495$	$2$	495.a	1.a	$1$	$3$	$3$	$3.953$	3.3.148.1	None	✓		✓	✓	165.2.a.c	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
495.2.a.f	$495$	$2$	495.a	1.a	$1$	$4$	$4$	$3.953$	4.4.48704.2	None	✓	✓	✓	✓	495.2.a.f	$1$	$0$	\(-2\)	\(0\)	\(-4\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
495.2.a.g	$495$	$2$	495.a	1.a	$1$	$4$	$4$	$3.953$	4.4.48704.2	None	✓	✓	✓	✓	495.2.a.f	$1$	$0$	\(2\)	\(0\)	\(4\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2+\beta _{2})q^{4}+q^{5}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(495))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(495)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 2}\)