Space of modular forms of level 2576, weight 2, and trivial character

• Label: 2576.2.a
• Level: $2576$
• Weight: $2$
• Character orbit: 2576.a
• Rep. character: $\chi_{2576}(1,\cdot)$
• Character field: $\Q$
• Dimension: $66$
• Newform subspaces: $31$
• Sturm bound: $768$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 2576 = 2^{4} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2576.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 31 \)
Sturm bound:			\(768\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2576))\).

	Total	New	Old
Modular forms	396	66	330
Cusp forms	373	66	307
Eisenstein series	23	0	23

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

\(2\)	\(7\)	\(23\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	\(10\)
\(+\)	\(-\)	\(+\)	\(-\)	\(10\)
\(+\)	\(-\)	\(-\)	\(+\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)	\(9\)
\(-\)	\(+\)	\(-\)	\(+\)	\(8\)
\(-\)	\(-\)	\(+\)	\(+\)	\(5\)
\(-\)	\(-\)	\(-\)	\(-\)	\(12\)
Plus space			\(+\)	\(25\)
Minus space			\(-\)	\(41\)

Trace form

\( 66 q + 4 q^{5} + 74 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2576))\) 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	23
2576.2.a.a	$2576$	$2$	2576.a	1.a	$1$	$1$	$1$	$20.569$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2q^{5}+q^{7}+6q^{9}-2q^{11}+\cdots\)
2576.2.a.b	$2576$	$2$	2576.a	1.a	$1$	$1$	$1$	$20.569$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-2\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{5}-q^{7}+q^{9}-6q^{11}+\cdots\)
2576.2.a.c	$2576$	$2$	2576.a	1.a	$1$	$1$	$1$	$20.569$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{7}+q^{9}-4q^{11}+6q^{17}+\cdots\)
2576.2.a.d	$2576$	$2$	2576.a	1.a	$1$	$1$	$1$	$20.569$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
2576.2.a.e	$2576$	$2$	2576.a	1.a	$1$	$1$	$1$	$20.569$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
2576.2.a.f	$2576$	$2$	2576.a	1.a	$1$	$1$	$1$	$20.569$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+4q^{5}-q^{7}+q^{9}-4q^{11}+\cdots\)
2576.2.a.g	$2576$	$2$	2576.a	1.a	$1$	$1$	$1$	$20.569$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}-2q^{9}+2q^{11}+\cdots\)
2576.2.a.h	$2576$	$2$	2576.a	1.a	$1$	$1$	$1$	$20.569$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}-2q^{9}+6q^{11}-3q^{13}+\cdots\)
2576.2.a.i	$2576$	$2$	2576.a	1.a	$1$	$1$	$1$	$20.569$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}-3q^{9}+4q^{11}+4q^{13}+\cdots\)
2576.2.a.j	$2576$	$2$	2576.a	1.a	$1$	$1$	$1$	$20.569$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}-3q^{9}-4q^{11}+6q^{13}+\cdots\)
2576.2.a.k	$2576$	$2$	2576.a	1.a	$1$	$1$	$1$	$20.569$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}-3q^{9}-4q^{13}-4q^{17}+\cdots\)
2576.2.a.l	$2576$	$2$	2576.a	1.a	$1$	$1$	$1$	$20.569$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}-2q^{9}+2q^{11}-3q^{13}+\cdots\)
2576.2.a.m	$2576$	$2$	2576.a	1.a	$1$	$1$	$1$	$20.569$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}+\cdots\)
2576.2.a.n	$2576$	$2$	2576.a	1.a	$1$	$1$	$1$	$20.569$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{7}+q^{9}-6q^{17}-6q^{19}+\cdots\)
2576.2.a.o	$2576$	$2$	2576.a	1.a	$1$	$1$	$1$	$20.569$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-4\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-4q^{5}+q^{7}+6q^{9}-2q^{11}+\cdots\)
2576.2.a.p	$2576$	$2$	2576.a	1.a	$1$	$1$	$1$	$20.569$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{7}+6q^{9}+6q^{11}+q^{13}+\cdots\)
2576.2.a.q	$2576$	$2$	2576.a	1.a	$1$	$2$	$2$	$20.569$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-2+\beta )q^{5}+q^{7}-q^{9}-2q^{11}+\cdots\)
2576.2.a.r	$2576$	$2$	2576.a	1.a	$1$	$2$	$2$	$20.569$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2q^{5}+q^{7}+(1+\beta )q^{9}-2\beta q^{11}+\cdots\)
2576.2.a.s	$2576$	$2$	2576.a	1.a	$1$	$2$	$2$	$20.569$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+q^{7}-2q^{9}-2\beta q^{11}+\cdots\)
2576.2.a.t	$2576$	$2$	2576.a	1.a	$1$	$2$	$2$	$20.569$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-1+\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
2576.2.a.u	$2576$	$2$	2576.a	1.a	$1$	$2$	$2$	$20.569$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(1-\beta )q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots\)
2576.2.a.v	$2576$	$2$	2576.a	1.a	$1$	$3$	$3$	$20.569$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(1-\beta _{1})q^{5}+q^{7}+\cdots\)
2576.2.a.w	$2576$	$2$	2576.a	1.a	$1$	$3$	$3$	$20.569$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(3\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(1-\beta _{2})q^{5}+q^{7}+\cdots\)
2576.2.a.x	$2576$	$2$	2576.a	1.a	$1$	$3$	$3$	$20.569$	3.3.568.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots\)
2576.2.a.y	$2576$	$2$	2576.a	1.a	$1$	$3$	$3$	$20.569$	3.3.148.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(2-2\beta _{1}-\beta _{2})q^{5}+q^{7}+\cdots\)
2576.2.a.z	$2576$	$2$	2576.a	1.a	$1$	$4$	$4$	$20.569$	4.4.34196.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{1}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
2576.2.a.ba	$2576$	$2$	2576.a	1.a	$1$	$4$	$4$	$20.569$	4.4.8468.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-\beta _{2}+\beta _{3})q^{5}-q^{7}+\cdots\)
2576.2.a.bb	$2576$	$2$	2576.a	1.a	$1$	$5$	$5$	$20.569$	5.5.6963152.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(2\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+\cdots\)
2576.2.a.bc	$2576$	$2$	2576.a	1.a	$1$	$5$	$5$	$20.569$	5.5.8580816.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(-5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1+\beta _{4})q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
2576.2.a.bd	$2576$	$2$	2576.a	1.a	$1$	$5$	$5$	$20.569$	5.5.2147108.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-5\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+(-1-\beta _{4})q^{5}-q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
2576.2.a.be	$2576$	$2$	2576.a	1.a	$1$	$5$	$5$	$20.569$	5.5.3385684.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(2\)	\(-5\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{3}+\beta _{1}q^{5}-q^{7}+(3-\beta _{4})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2576))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2576)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(644))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1288))\)\(^{\oplus 2}\)