Space of modular forms of level 2448, weight 2, and trivial character

• Label: 2448.2.a
• Level: $2448$
• Weight: $2$
• Character orbit: 2448.a
• Rep. character: $\chi_{2448}(1,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $29$
• Sturm bound: $864$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2448.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 29 \)
Sturm bound:			\(864\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2448))\).

	Total	New	Old
Modular forms	456	40	416
Cusp forms	409	40	369
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.

\(2\)	\(3\)	\(17\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(52\)	\(4\)	\(48\)		\(47\)	\(4\)	\(43\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(60\)	\(4\)	\(56\)		\(54\)	\(4\)	\(50\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(58\)	\(7\)	\(51\)		\(52\)	\(7\)	\(45\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(58\)	\(5\)	\(53\)		\(52\)	\(5\)	\(47\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(62\)	\(4\)	\(58\)		\(56\)	\(4\)	\(52\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(54\)	\(4\)	\(50\)		\(48\)	\(4\)	\(44\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(56\)	\(5\)	\(51\)		\(50\)	\(5\)	\(45\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(56\)	\(7\)	\(49\)		\(50\)	\(7\)	\(43\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(220\)	\(18\)	\(202\)		\(197\)	\(18\)	\(179\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(236\)	\(22\)	\(214\)		\(212\)	\(22\)	\(190\)		\(24\)	\(0\)	\(24\)

Trace form

40 * q - 6 * q^7 - 10 * q^11 - 4 * q^19 + 2 * q^23 + 48 * q^25 + 16 * q^29 + 2 * q^31 - 12 * q^35 + 8 * q^37 - 8 * q^41 + 20 * q^43 - 24 * q^47 + 32 * q^49 + 8 * q^53 + 4 * q^55 + 12 * q^59 + 8 * q^65 - 32 * q^67 + 10 * q^71 + 16 * q^77 - 42 * q^79 - 20 * q^83 - 24 * q^89 - 8 * q^91 + 8 * q^95 - 24 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2448))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	17
2448.2.a.a	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				612.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-2q^{7}+3q^{11}-q^{13}+q^{17}+\cdots\)
2448.2.a.b	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				408.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-q^{11}+3q^{13}+q^{17}-q^{19}+\cdots\)
2448.2.a.c	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				51.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+4q^{7}-3q^{11}-q^{13}+q^{17}+\cdots\)
2448.2.a.d	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				408.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}+4q^{11}+6q^{13}-q^{17}+\cdots\)
2448.2.a.e	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				204.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+5q^{11}-5q^{13}-q^{17}-q^{19}+\cdots\)
2448.2.a.f	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				1224.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-3q^{11}-q^{13}-q^{17}+\cdots\)
2448.2.a.g	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				153.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+3q^{11}-5q^{13}-q^{17}+\cdots\)
2448.2.a.h	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				408.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+2q^{13}+q^{17}-4q^{19}+2q^{23}+\cdots\)
2448.2.a.i	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				102.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+2q^{13}+q^{17}+4q^{19}-6q^{23}+\cdots\)
2448.2.a.j	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				136.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{11}-6q^{13}+q^{17}-4q^{19}+4q^{23}+\cdots\)
2448.2.a.k	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				34.2.a.a	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}+6q^{11}+2q^{13}+q^{17}+4q^{19}+\cdots\)
2448.2.a.l	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				204.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}+3q^{11}+3q^{13}+q^{17}+\cdots\)
2448.2.a.m	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				153.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-3q^{11}-5q^{13}+q^{17}+\cdots\)
2448.2.a.n	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				1224.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+3q^{11}-q^{13}+q^{17}+\cdots\)
2448.2.a.o	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				17.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{7}-2q^{13}-q^{17}+4q^{19}+\cdots\)
2448.2.a.p	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				102.2.a.c	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{11}-2q^{13}-q^{17}-4q^{19}+\cdots\)
2448.2.a.q	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				136.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{7}-6q^{11}+2q^{13}-q^{17}+\cdots\)
2448.2.a.r	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				612.2.a.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-2q^{7}-3q^{11}-q^{13}-q^{17}+\cdots\)
2448.2.a.s	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				408.2.a.b	$1$	$0$	\(0\)	\(0\)	\(3\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+4q^{7}+q^{11}-5q^{13}-q^{17}+\cdots\)
2448.2.a.t	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	\(\Q\)	None	✓				102.2.a.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+2q^{7}-6q^{13}+q^{17}-4q^{19}+\cdots\)
2448.2.a.u	$2448$	$2$	2448.a	1.a	$1$	$2$	$2$	$19.547$	\(\Q(\sqrt{5}) \)	None	✓				136.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(-2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-2q^{5}+(-1+\beta )q^{7}+(1-\beta )q^{11}+\cdots\)
2448.2.a.v	$2448$	$2$	2448.a	1.a	$1$	$2$	$2$	$19.547$	\(\Q(\sqrt{17}) \)	None	✓		✓		51.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+(-1+\beta )q^{11}+(3-\beta )q^{13}+\cdots\)
2448.2.a.w	$2448$	$2$	2448.a	1.a	$1$	$2$	$2$	$19.547$	\(\Q(\sqrt{6}) \)	None	✓		✓		306.2.a.e	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(-2+\beta )q^{7}+2\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
2448.2.a.x	$2448$	$2$	2448.a	1.a	$1$	$2$	$2$	$19.547$	\(\Q(\sqrt{6}) \)	None	✓		✓		306.2.a.e	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(-2-\beta )q^{7}+2\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
2448.2.a.y	$2448$	$2$	2448.a	1.a	$1$	$2$	$2$	$19.547$	\(\Q(\sqrt{3}) \)	None	✓		✓		68.2.a.a	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{5}+(1+\beta )q^{7}+(-3+\beta )q^{11}+\cdots\)
2448.2.a.z	$2448$	$2$	2448.a	1.a	$1$	$2$	$2$	$19.547$	\(\Q(\sqrt{57}) \)	None	✓				408.2.a.f	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-8\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-4q^{7}+(-2+\beta )q^{11}+\beta q^{13}+\cdots\)
2448.2.a.ba	$2448$	$2$	2448.a	1.a	$1$	$2$	$2$	$19.547$	\(\Q(\sqrt{17}) \)	None	✓		✓		408.2.a.e	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(2-2\beta )q^{7}+(-4-\beta )q^{11}+\cdots\)
2448.2.a.bb	$2448$	$2$	2448.a	1.a	$1$	$3$	$3$	$19.547$	3.3.1304.1	None	✓		✓		1224.2.a.l	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{2})q^{7}+(-1+\cdots)q^{11}+\cdots\)
2448.2.a.bc	$2448$	$2$	2448.a	1.a	$1$	$3$	$3$	$19.547$	3.3.1304.1	None	✓		✓		1224.2.a.l	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{5}+(-1-\beta _{2})q^{7}+(1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2448))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2448)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(153))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(306))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(408))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(612))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(816))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1224))\)\(^{\oplus 2}\)