Space of modular forms of level 2464, weight 2, and trivial character

• Label: 2464.2.a
• Level: $2464$
• Weight: $2$
• Character orbit: 2464.a
• Rep. character: $\chi_{2464}(1,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $26$
• Sturm bound: $768$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2464 = 2^{5} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2464.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 26 \)
Sturm bound:			\(768\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2464))\).

	Total	New	Old
Modular forms	400	60	340
Cusp forms	369	60	309
Eisenstein series	31	0	31

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

\(2\)	\(7\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(8\)
\(+\)	\(+\)	\(-\)	$-$	\(9\)
\(+\)	\(-\)	\(+\)	$-$	\(8\)
\(+\)	\(-\)	\(-\)	$+$	\(5\)
\(-\)	\(+\)	\(+\)	$-$	\(7\)
\(-\)	\(+\)	\(-\)	$+$	\(6\)
\(-\)	\(-\)	\(+\)	$+$	\(7\)
\(-\)	\(-\)	\(-\)	$-$	\(10\)
Plus space			\(+\)	\(26\)
Minus space			\(-\)	\(34\)

Trace form

\( 60 q - 8 q^{5} + 60 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2464))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7	11
2464.2.a.a	$2464$	$2$	2464.a	1.a	$1$	$1$	$1$	$19.675$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{5}-q^{7}+q^{9}+q^{11}+4q^{13}+\cdots\)
2464.2.a.b	$2464$	$2$	2464.a	1.a	$1$	$1$	$1$	$19.675$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{7}+q^{9}+q^{11}-6q^{17}+\cdots\)
2464.2.a.c	$2464$	$2$	2464.a	1.a	$1$	$1$	$1$	$19.675$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+4q^{5}-q^{7}+q^{9}+q^{11}+4q^{13}+\cdots\)
2464.2.a.d	$2464$	$2$	2464.a	1.a	$1$	$1$	$1$	$19.675$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-q^{7}-2q^{9}-q^{11}+6q^{13}+\cdots\)
2464.2.a.e	$2464$	$2$	2464.a	1.a	$1$	$1$	$1$	$19.675$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}-2q^{9}-q^{11}-2q^{13}+\cdots\)
2464.2.a.f	$2464$	$2$	2464.a	1.a	$1$	$1$	$1$	$19.675$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-3q^{9}+q^{11}-2q^{13}+4q^{17}+\cdots\)
2464.2.a.g	$2464$	$2$	2464.a	1.a	$1$	$1$	$1$	$19.675$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{9}-q^{11}-2q^{13}+4q^{17}+\cdots\)
2464.2.a.h	$2464$	$2$	2464.a	1.a	$1$	$1$	$1$	$19.675$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{7}-2q^{9}+q^{11}+6q^{13}+\cdots\)
2464.2.a.i	$2464$	$2$	2464.a	1.a	$1$	$1$	$1$	$19.675$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}-2q^{9}+q^{11}-2q^{13}+\cdots\)
2464.2.a.j	$2464$	$2$	2464.a	1.a	$1$	$1$	$1$	$19.675$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}+q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
2464.2.a.k	$2464$	$2$	2464.a	1.a	$1$	$1$	$1$	$19.675$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{7}+q^{9}-q^{11}-6q^{17}+\cdots\)
2464.2.a.l	$2464$	$2$	2464.a	1.a	$1$	$1$	$1$	$19.675$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(4\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+4q^{5}+q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
2464.2.a.m	$2464$	$2$	2464.a	1.a	$1$	$2$	$2$	$19.675$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+2\beta q^{5}-q^{7}+(1-2\beta )q^{9}+\cdots\)
2464.2.a.n	$2464$	$2$	2464.a	1.a	$1$	$2$	$2$	$19.675$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+\beta q^{5}+q^{7}+(1+\beta )q^{9}-q^{11}+\cdots\)
2464.2.a.o	$2464$	$2$	2464.a	1.a	$1$	$2$	$2$	$19.675$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+\beta q^{5}-q^{7}+(1+\beta )q^{9}+q^{11}+\cdots\)
2464.2.a.p	$2464$	$2$	2464.a	1.a	$1$	$2$	$2$	$19.675$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-2\beta q^{5}+q^{7}+(1+2\beta )q^{9}+\cdots\)
2464.2.a.q	$2464$	$2$	2464.a	1.a	$1$	$3$	$3$	$19.675$	3.3.316.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+q^{7}+\beta _{2}q^{9}+\cdots\)
2464.2.a.r	$2464$	$2$	2464.a	1.a	$1$	$3$	$3$	$19.675$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}-q^{7}+\beta _{2}q^{9}+\cdots\)
2464.2.a.s	$2464$	$2$	2464.a	1.a	$1$	$4$	$4$	$19.675$	4.4.8468.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-5\)	\(-4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{3})q^{5}-q^{7}+\beta _{3}q^{9}+\cdots\)
2464.2.a.t	$2464$	$2$	2464.a	1.a	$1$	$4$	$4$	$19.675$	4.4.10273.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(4\)		$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{1}q^{5}+q^{7}+(2-\beta _{2})q^{9}+\cdots\)
2464.2.a.u	$2464$	$2$	2464.a	1.a	$1$	$4$	$4$	$19.675$	4.4.2777.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(5\)	\(-4\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(1-\beta _{1})q^{5}-q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
2464.2.a.v	$2464$	$2$	2464.a	1.a	$1$	$4$	$4$	$19.675$	4.4.8468.1	None	✓	$1$	$1$	\(0\)	\(1\)	\(-5\)	\(4\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+q^{7}+\beta _{3}q^{9}+\cdots\)
2464.2.a.w	$2464$	$2$	2464.a	1.a	$1$	$4$	$4$	$19.675$	4.4.10273.1	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-4\)		$+$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{1}q^{5}-q^{7}+(2-\beta _{2})q^{9}+\cdots\)
2464.2.a.x	$2464$	$2$	2464.a	1.a	$1$	$4$	$4$	$19.675$	4.4.2777.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(5\)	\(4\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(1-\beta _{1})q^{5}+q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
2464.2.a.y	$2464$	$2$	2464.a	1.a	$1$	$5$	$5$	$19.675$	5.5.2042356.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-1\)	\(5\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{3}+\beta _{3}q^{5}+q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
2464.2.a.z	$2464$	$2$	2464.a	1.a	$1$	$5$	$5$	$19.675$	5.5.2042356.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(-5\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{3}+\beta _{3}q^{5}-q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2464))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2464)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(616))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1232))\)\(^{\oplus 2}\)