Space of modular forms of level 5265, weight 2, and trivial character

• Label: 5265.2.a
• Level: $5265$
• Weight: $2$
• Character orbit: 5265.a
• Rep. character: $\chi_{5265}(1,\cdot)$
• Character field: $\Q$
• Dimension: $192$
• Newform subspaces: $38$
• Sturm bound: $1512$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 5265 = 3^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5265.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 38 \)
Sturm bound:			\(1512\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5265))\).

	Total	New	Old
Modular forms	780	192	588
Cusp forms	733	192	541
Eisenstein series	47	0	47

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

\(3\)	\(5\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(25\)
\(+\)	\(+\)	\(-\)	$-$	\(25\)
\(+\)	\(-\)	\(+\)	$-$	\(27\)
\(+\)	\(-\)	\(-\)	$+$	\(19\)
\(-\)	\(+\)	\(+\)	$-$	\(23\)
\(-\)	\(+\)	\(-\)	$+$	\(23\)
\(-\)	\(-\)	\(+\)	$+$	\(21\)
\(-\)	\(-\)	\(-\)	$-$	\(29\)
Plus space			\(+\)	\(88\)
Minus space			\(-\)	\(104\)

Trace form

\( 192 q + 192 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5265))\) 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	13
5265.2.a.a	$5265$	$2$	5265.a	1.a	$1$	$1$	$1$	$42.041$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-q^{5}+2q^{10}+4q^{11}+\cdots\)
5265.2.a.b	$5265$	$2$	5265.a	1.a	$1$	$1$	$1$	$42.041$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-q^{5}+2q^{10}+5q^{11}+\cdots\)
5265.2.a.c	$5265$	$2$	5265.a	1.a	$1$	$1$	$1$	$42.041$	\(\Q\)	None	✓	$1$	$2$	\(-2\)	\(0\)	\(1\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}-4q^{7}-2q^{10}+\cdots\)
5265.2.a.d	$5265$	$2$	5265.a	1.a	$1$	$1$	$1$	$42.041$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}+q^{10}+\cdots\)
5265.2.a.e	$5265$	$2$	5265.a	1.a	$1$	$1$	$1$	$42.041$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}+2q^{7}+3q^{8}+q^{10}+\cdots\)
5265.2.a.f	$5265$	$2$	5265.a	1.a	$1$	$1$	$1$	$42.041$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}+3q^{7}+3q^{8}-q^{10}+\cdots\)
5265.2.a.g	$5265$	$2$	5265.a	1.a	$1$	$1$	$1$	$42.041$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{5}-4q^{7}+q^{13}+4q^{16}+\cdots\)
5265.2.a.h	$5265$	$2$	5265.a	1.a	$1$	$1$	$1$	$42.041$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{5}+2q^{7}+3q^{11}+q^{13}+\cdots\)
5265.2.a.i	$5265$	$2$	5265.a	1.a	$1$	$1$	$1$	$42.041$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}-4q^{7}+q^{13}+4q^{16}+\cdots\)
5265.2.a.j	$5265$	$2$	5265.a	1.a	$1$	$1$	$1$	$42.041$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}+2q^{7}-3q^{11}+q^{13}+\cdots\)
5265.2.a.k	$5265$	$2$	5265.a	1.a	$1$	$1$	$1$	$42.041$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}+3q^{7}-3q^{8}-q^{10}+\cdots\)
5265.2.a.l	$5265$	$2$	5265.a	1.a	$1$	$1$	$1$	$42.041$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-q^{7}-3q^{8}+q^{10}+\cdots\)
5265.2.a.m	$5265$	$2$	5265.a	1.a	$1$	$1$	$1$	$42.041$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}+2q^{7}-3q^{8}+q^{10}+\cdots\)
5265.2.a.n	$5265$	$2$	5265.a	1.a	$1$	$1$	$1$	$42.041$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-1\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}-4q^{7}-2q^{10}+\cdots\)
5265.2.a.o	$5265$	$2$	5265.a	1.a	$1$	$1$	$1$	$42.041$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{5}+2q^{10}-5q^{11}+\cdots\)
5265.2.a.p	$5265$	$2$	5265.a	1.a	$1$	$1$	$1$	$42.041$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{5}+2q^{10}-4q^{11}+\cdots\)
5265.2.a.q	$5265$	$2$	5265.a	1.a	$1$	$2$	$2$	$42.041$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}-\beta q^{7}+3q^{8}-q^{10}+\cdots\)
5265.2.a.r	$5265$	$2$	5265.a	1.a	$1$	$2$	$2$	$42.041$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}+\beta q^{7}-3q^{8}-q^{10}+\cdots\)
5265.2.a.s	$5265$	$2$	5265.a	1.a	$1$	$3$	$3$	$42.041$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(3\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
5265.2.a.t	$5265$	$2$	5265.a	1.a	$1$	$3$	$3$	$42.041$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$0$	\(3\)	\(0\)	\(-3\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
5265.2.a.u	$5265$	$2$	5265.a	1.a	$1$	$4$	$4$	$42.041$	4.4.16609.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(-6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-2-\beta _{2}+\cdots)q^{7}+\cdots\)
5265.2.a.v	$5265$	$2$	5265.a	1.a	$1$	$4$	$4$	$42.041$	4.4.16609.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(-2-\beta _{2}+\cdots)q^{7}+\cdots\)
5265.2.a.w	$5265$	$2$	5265.a	1.a	$1$	$6$	$6$	$42.041$	6.6.585163476.1	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-6\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)
5265.2.a.x	$5265$	$2$	5265.a	1.a	$1$	$6$	$6$	$42.041$	6.6.585163476.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(6\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+(1+\cdots)q^{7}+\cdots\)
5265.2.a.y	$5265$	$2$	5265.a	1.a	$1$	$7$	$7$	$42.041$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-7\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots\)
5265.2.a.z	$5265$	$2$	5265.a	1.a	$1$	$7$	$7$	$42.041$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(7\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots\)
5265.2.a.ba	$5265$	$2$	5265.a	1.a	$1$	$8$	$8$	$42.041$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(8\)	\(-11\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
5265.2.a.bb	$5265$	$2$	5265.a	1.a	$1$	$8$	$8$	$42.041$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(8\)	\(-6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1+\beta _{6}+\cdots)q^{7}+\cdots\)
5265.2.a.bc	$5265$	$2$	5265.a	1.a	$1$	$8$	$8$	$42.041$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-8\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
5265.2.a.bd	$5265$	$2$	5265.a	1.a	$1$	$8$	$8$	$42.041$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(8\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
5265.2.a.be	$5265$	$2$	5265.a	1.a	$1$	$8$	$8$	$42.041$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-8\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(-1+\beta _{6}+\cdots)q^{7}+\cdots\)
5265.2.a.bf	$5265$	$2$	5265.a	1.a	$1$	$8$	$8$	$42.041$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(3\)	\(0\)	\(-8\)	\(-11\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
5265.2.a.bg	$5265$	$2$	5265.a	1.a	$1$	$13$	$13$	$42.041$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(13\)	\(10\)		$+$	$-$	$+$	$-$	$3^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots\)
5265.2.a.bh	$5265$	$2$	5265.a	1.a	$1$	$13$	$13$	$42.041$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-13\)	\(10\)		$-$	$+$	$+$	$-$	$3^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots\)
5265.2.a.bi	$5265$	$2$	5265.a	1.a	$1$	$14$	$14$	$42.041$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-14\)	\(4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}-\beta _{3}q^{7}+\cdots\)
5265.2.a.bj	$5265$	$2$	5265.a	1.a	$1$	$14$	$14$	$42.041$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(14\)	\(4\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}-\beta _{3}q^{7}+\cdots\)
5265.2.a.bk	$5265$	$2$	5265.a	1.a	$1$	$15$	$15$	$42.041$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-15\)	\(10\)		$+$	$+$	$-$	$-$	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1-\beta _{6}+\cdots)q^{7}+\cdots\)
5265.2.a.bl	$5265$	$2$	5265.a	1.a	$1$	$15$	$15$	$42.041$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(15\)	\(10\)		$-$	$-$	$-$	$-$	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1-\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5265))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5265)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(351))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(405))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(585))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1053))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1755))\)\(^{\oplus 2}\)