Space of modular forms of level 4815, weight 2, and trivial character

• Label: 4815.2.a
• Level: $4815$
• Weight: $2$
• Character orbit: 4815.a
• Rep. character: $\chi_{4815}(1,\cdot)$
• Character field: $\Q$
• Dimension: $178$
• Newform subspaces: $24$
• Sturm bound: $1296$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 4815 = 3^{2} \cdot 5 \cdot 107 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4815.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 24 \)
Sturm bound:			\(1296\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4815))\).

	Total	New	Old
Modular forms	656	178	478
Cusp forms	641	178	463
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.

\(3\)	\(5\)	\(107\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(11\)
\(+\)	\(+\)	\(-\)	\(-\)	\(25\)
\(+\)	\(-\)	\(+\)	\(-\)	\(25\)
\(+\)	\(-\)	\(-\)	\(+\)	\(11\)
\(-\)	\(+\)	\(+\)	\(-\)	\(27\)
\(-\)	\(+\)	\(-\)	\(+\)	\(26\)
\(-\)	\(-\)	\(+\)	\(+\)	\(20\)
\(-\)	\(-\)	\(-\)	\(-\)	\(33\)
Plus space			\(+\)	\(68\)
Minus space			\(-\)	\(110\)

Trace form

\( 178 q + 182 q^{4} + 4 q^{7} + 12 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4815))\) 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	107
4815.2.a.a	$4815$	$2$	4815.a	1.a	$1$	$1$	$1$	$38.448$	\(\Q\)	None	✓				1605.2.a.e	$1$	$1$	\(-2\)	\(0\)	\(-1\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-q^{5}+3q^{7}+2q^{10}+\cdots\)
4815.2.a.b	$4815$	$2$	4815.a	1.a	$1$	$1$	$1$	$38.448$	\(\Q\)	None	✓	✓			4815.2.a.b	$1$	$0$	\(-2\)	\(0\)	\(-1\)	\(5\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-q^{5}+5q^{7}+2q^{10}+\cdots\)
4815.2.a.c	$4815$	$2$	4815.a	1.a	$1$	$1$	$1$	$38.448$	\(\Q\)	None	✓				1605.2.a.d	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}-4q^{7}+3q^{8}-q^{10}+\cdots\)
4815.2.a.d	$4815$	$2$	4815.a	1.a	$1$	$1$	$1$	$38.448$	\(\Q\)	None	✓				1605.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{5}-q^{7}+6q^{11}+2q^{13}+\cdots\)
4815.2.a.e	$4815$	$2$	4815.a	1.a	$1$	$1$	$1$	$38.448$	\(\Q\)	None	✓				1605.2.a.b	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}+4q^{7}-3q^{8}-q^{10}+\cdots\)
4815.2.a.f	$4815$	$2$	4815.a	1.a	$1$	$1$	$1$	$38.448$	\(\Q\)	None	✓				1605.2.a.a	$1$	$0$	\(2\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{5}+q^{7}+2q^{10}+\cdots\)
4815.2.a.g	$4815$	$2$	4815.a	1.a	$1$	$1$	$1$	$38.448$	\(\Q\)	None	✓	✓			4815.2.a.b	$1$	$0$	\(2\)	\(0\)	\(1\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{5}+5q^{7}+2q^{10}+\cdots\)
4815.2.a.h	$4815$	$2$	4815.a	1.a	$1$	$3$	$3$	$38.448$	\(\Q(\zeta_{18})^+\)	None	✓				1605.2.a.f	$1$	$0$	\(-3\)	\(0\)	\(3\)	\(9\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
4815.2.a.i	$4815$	$2$	4815.a	1.a	$1$	$3$	$3$	$38.448$	\(\Q(\zeta_{14})^+\)	None	✓				535.2.a.a	$1$	$0$	\(2\)	\(0\)	\(-3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
4815.2.a.j	$4815$	$2$	4815.a	1.a	$1$	$4$	$4$	$38.448$	4.4.1957.1	None	✓				1605.2.a.g	$1$	$1$	\(3\)	\(0\)	\(-4\)	\(-8\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(1-\beta _{1}-\beta _{3})q^{4}-q^{5}+\cdots\)
4815.2.a.k	$4815$	$2$	4815.a	1.a	$1$	$5$	$5$	$38.448$	5.5.240133.1	None	✓				1605.2.a.j	$1$	$1$	\(-2\)	\(0\)	\(-5\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
4815.2.a.l	$4815$	$2$	4815.a	1.a	$1$	$5$	$5$	$38.448$	5.5.81509.1	None	✓				1605.2.a.i	$1$	$1$	\(1\)	\(0\)	\(5\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
4815.2.a.m	$4815$	$2$	4815.a	1.a	$1$	$5$	$5$	$38.448$	5.5.805501.1	None	✓				1605.2.a.h	$1$	$1$	\(1\)	\(0\)	\(5\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
4815.2.a.n	$4815$	$2$	4815.a	1.a	$1$	$8$	$8$	$38.448$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				535.2.a.b	$1$	$0$	\(4\)	\(0\)	\(8\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{5}+\beta _{6})q^{4}+q^{5}+\cdots\)
4815.2.a.o	$4815$	$2$	4815.a	1.a	$1$	$9$	$9$	$38.448$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		535.2.a.c	$1$	$1$	\(-5\)	\(0\)	\(9\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4815.2.a.p	$4815$	$2$	4815.a	1.a	$1$	$10$	$10$	$38.448$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				1605.2.a.k	$1$	$0$	\(-2\)	\(0\)	\(10\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(\beta _{5}+\beta _{7}+\cdots)q^{7}+\cdots\)
4815.2.a.q	$4815$	$2$	4815.a	1.a	$1$	$11$	$11$	$38.448$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓	✓	✓	4815.2.a.q	$1$	$1$	\(-1\)	\(0\)	\(11\)	\(-4\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}-\beta _{9}q^{7}-\beta _{3}q^{8}+\cdots\)
4815.2.a.r	$4815$	$2$	4815.a	1.a	$1$	$11$	$11$	$38.448$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓	✓	✓	4815.2.a.q	$1$	$1$	\(1\)	\(0\)	\(-11\)	\(-4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}-\beta _{9}q^{7}+\beta _{3}q^{8}+\cdots\)
4815.2.a.s	$4815$	$2$	4815.a	1.a	$1$	$11$	$11$	$38.448$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓				1605.2.a.l	$1$	$0$	\(4\)	\(0\)	\(-11\)	\(-9\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(-2+\cdots)q^{7}+\cdots\)
4815.2.a.t	$4815$	$2$	4815.a	1.a	$1$	$11$	$11$	$38.448$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓		✓		1605.2.a.m	$1$	$0$	\(4\)	\(0\)	\(11\)	\(-4\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+\beta _{7}q^{7}+\cdots\)
4815.2.a.u	$4815$	$2$	4815.a	1.a	$1$	$12$	$12$	$38.448$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		1605.2.a.n	$1$	$0$	\(-3\)	\(0\)	\(-12\)	\(7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots\)
4815.2.a.v	$4815$	$2$	4815.a	1.a	$1$	$15$	$15$	$38.448$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓		✓		535.2.a.d	$1$	$1$	\(-4\)	\(0\)	\(-15\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{9}q^{7}+\cdots\)
4815.2.a.w	$4815$	$2$	4815.a	1.a	$1$	$24$	$24$	$38.448$		None	✓	✓	✓		4815.2.a.w	$1$	$0$	\(-3\)	\(0\)	\(24\)	\(3\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
4815.2.a.x	$4815$	$2$	4815.a	1.a	$1$	$24$	$24$	$38.448$		None	✓	✓	✓		4815.2.a.w	$1$	$0$	\(3\)	\(0\)	\(-24\)	\(3\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4815))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4815)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(107))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(321))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(535))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(963))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1605))\)\(^{\oplus 2}\)