Space of modular forms of level 495, weight 6, and trivial character

• Label: 495.6.a
• Level: $495$
• Weight: $6$
• Character orbit: 495.a
• Rep. character: $\chi_{495}(1,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $16$
• Sturm bound: $432$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	495.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(432\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(495))\).

	Total	New	Old
Modular forms	368	82	286
Cusp forms	352	82	270
Eisenstein series	16	0	16

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.
\(+\)	\(+\)	\(+\)	\(+\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	\(10\)
\(+\)	\(-\)	\(+\)	\(-\)	\(10\)
\(+\)	\(-\)	\(-\)	\(+\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)	\(13\)
\(-\)	\(+\)	\(-\)	\(+\)	\(11\)
\(-\)	\(-\)	\(+\)	\(+\)	\(12\)
\(-\)	\(-\)	\(-\)	\(-\)	\(14\)
Plus space			\(+\)	\(35\)
Minus space			\(-\)	\(47\)

Trace form

\( 82 q + 1268 q^{4} + 50 q^{5} - 44 q^{7} - 852 q^{8} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(495))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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
495.6.a.a	$495$	$6$	495.a	1.a	$1$	$3$	$3$	$79.390$	3.3.307532.1	None	✓	$1$	$1$	\(-7\)	\(0\)	\(75\)	\(92\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{1})q^{2}+(24+2\beta _{1}+\beta _{2})q^{4}+\cdots\)
495.6.a.b	$495$	$6$	495.a	1.a	$1$	$3$	$3$	$79.390$	3.3.18257.1	None	✓	$1$	$0$	\(-2\)	\(0\)	\(-75\)	\(-68\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-14-\beta _{1}+\beta _{2})q^{4}+\cdots\)
495.6.a.c	$495$	$6$	495.a	1.a	$1$	$3$	$3$	$79.390$	3.3.788.1	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-75\)	\(152\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(-8-4\beta _{1})q^{4}-5^{2}q^{5}+\cdots\)
495.6.a.d	$495$	$6$	495.a	1.a	$1$	$3$	$3$	$79.390$	3.3.3368.1	None	✓	$1$	$1$	\(2\)	\(0\)	\(75\)	\(-232\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(8+4\beta _{2})q^{4}+5^{2}q^{5}+\cdots\)
495.6.a.e	$495$	$6$	495.a	1.a	$1$	$3$	$3$	$79.390$	3.3.34253.1	None	✓	$1$	$1$	\(7\)	\(0\)	\(-75\)	\(-172\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(2+\beta _{1})q^{2}+(7+4\beta _{1}+\beta _{2})q^{4}-5^{2}q^{5}+\cdots\)
495.6.a.f	$495$	$6$	495.a	1.a	$1$	$3$	$3$	$79.390$	3.3.21865.1	None	✓	$1$	$0$	\(7\)	\(0\)	\(-75\)	\(-102\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta _{2})q^{2}+(12+4\beta _{1}+\beta _{2})q^{4}+\cdots\)
495.6.a.g	$495$	$6$	495.a	1.a	$1$	$4$	$4$	$79.390$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(5\)	\(0\)	\(100\)	\(-90\)		$-$	$-$	$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(15+\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\cdots\)
495.6.a.h	$495$	$6$	495.a	1.a	$1$	$5$	$5$	$79.390$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(-9\)	\(0\)	\(-125\)	\(70\)		$-$	$+$	$-$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{2}+(24-3\beta _{1}+\beta _{2})q^{4}+\cdots\)
495.6.a.i	$495$	$6$	495.a	1.a	$1$	$5$	$5$	$79.390$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(125\)	\(116\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(5^{2}+\beta _{1}+\beta _{3})q^{4}+5^{2}q^{5}+\cdots\)
495.6.a.j	$495$	$6$	495.a	1.a	$1$	$5$	$5$	$79.390$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(125\)	\(184\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2^{4}+\beta _{2})q^{4}+5^{2}q^{5}+(37+\cdots)q^{7}+\cdots\)
495.6.a.k	$495$	$6$	495.a	1.a	$1$	$6$	$6$	$79.390$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(-5\)	\(0\)	\(150\)	\(-80\)		$+$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(9-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
495.6.a.l	$495$	$6$	495.a	1.a	$1$	$6$	$6$	$79.390$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(150\)	\(-66\)		$-$	$-$	$+$	$+$	$2\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(20-\beta _{1}+\beta _{3}+\beta _{5})q^{4}+\cdots\)
495.6.a.m	$495$	$6$	495.a	1.a	$1$	$6$	$6$	$79.390$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(5\)	\(0\)	\(-150\)	\(-80\)		$+$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(9-2\beta _{1}+\beta _{2})q^{4}-5^{2}q^{5}+\cdots\)
495.6.a.n	$495$	$6$	495.a	1.a	$1$	$7$	$7$	$79.390$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-175\)	\(0\)		$-$	$+$	$+$	$-$	$2^{6}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(28+\beta _{2})q^{4}-5^{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
495.6.a.o	$495$	$6$	495.a	1.a	$1$	$10$	$10$	$79.390$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(-3\)	\(0\)	\(-250\)	\(116\)		$+$	$+$	$-$	$-$	$2^{4}\cdot 3^{6}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(18+\beta _{2})q^{4}-5^{2}q^{5}+(12+\cdots)q^{7}+\cdots\)
495.6.a.p	$495$	$6$	495.a	1.a	$1$	$10$	$10$	$79.390$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(0\)	\(250\)	\(116\)		$+$	$-$	$+$	$-$	$2^{4}\cdot 3^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(18+\beta _{2})q^{4}+5^{2}q^{5}+(12+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(495))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(495)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 2}\)