Space of modular forms of level 3264, weight 2, and trivial character

• Label: 3264.2.a
• Level: $3264$
• Weight: $2$
• Character orbit: 3264.a
• Rep. character: $\chi_{3264}(1,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $46$
• Sturm bound: $1152$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 3264 = 2^{6} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3264.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 46 \)
Sturm bound:			\(1152\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3264))\).

	Total	New	Old
Modular forms	600	64	536
Cusp forms	553	64	489
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	Dim
\(+\)	\(+\)	\(+\)	$+$	\(7\)
\(+\)	\(+\)	\(-\)	$-$	\(10\)
\(+\)	\(-\)	\(+\)	$-$	\(9\)
\(+\)	\(-\)	\(-\)	$+$	\(6\)
\(-\)	\(+\)	\(+\)	$-$	\(9\)
\(-\)	\(+\)	\(-\)	$+$	\(6\)
\(-\)	\(-\)	\(+\)	$+$	\(7\)
\(-\)	\(-\)	\(-\)	$-$	\(10\)
Plus space			\(+\)	\(26\)
Minus space			\(-\)	\(38\)

Trace form

\( 64 q + 64 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3264))\) 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	3	17
3264.2.a.a	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-4q^{7}+q^{9}+3q^{11}+\cdots\)
3264.2.a.b	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+q^{9}-q^{11}-3q^{13}+\cdots\)
3264.2.a.c	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(-2\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
3264.2.a.d	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
3264.2.a.e	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}+5q^{11}+q^{13}+\cdots\)
3264.2.a.f	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}-5q^{11}+5q^{13}+\cdots\)
3264.2.a.g	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}+6q^{13}-q^{17}+\cdots\)
3264.2.a.h	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-2q^{13}-q^{17}+\cdots\)
3264.2.a.i	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-2q^{13}-q^{17}+\cdots\)
3264.2.a.j	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-4q^{7}+q^{9}+3q^{11}-3q^{13}+\cdots\)
3264.2.a.k	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
3264.2.a.l	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}+5q^{11}+5q^{13}+\cdots\)
3264.2.a.m	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
3264.2.a.n	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-4q^{7}+q^{9}-q^{11}+5q^{13}+\cdots\)
3264.2.a.o	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-2q^{7}+q^{9}-3q^{11}+\cdots\)
3264.2.a.p	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}+2q^{7}+q^{9}+6q^{13}+\cdots\)
3264.2.a.q	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{9}+q^{11}-3q^{13}+\cdots\)
3264.2.a.r	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+4q^{7}+q^{9}-3q^{11}+\cdots\)
3264.2.a.s	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
3264.2.a.t	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
3264.2.a.u	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+5q^{11}+5q^{13}+\cdots\)
3264.2.a.v	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}-5q^{11}+q^{13}+\cdots\)
3264.2.a.w	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}-2q^{13}-q^{17}+\cdots\)
3264.2.a.x	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}-2q^{13}-q^{17}+\cdots\)
3264.2.a.y	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}+6q^{13}-q^{17}+\cdots\)
3264.2.a.z	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}-5q^{11}+5q^{13}+\cdots\)
3264.2.a.ba	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
3264.2.a.bb	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+4q^{7}+q^{9}-3q^{11}-3q^{13}+\cdots\)
3264.2.a.bc	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
3264.2.a.bd	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+2q^{7}+q^{9}+3q^{11}+\cdots\)
3264.2.a.be	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+4q^{7}+q^{9}+q^{11}+5q^{13}+\cdots\)
3264.2.a.bf	$3264$	$2$	3264.a	1.a	$1$	$1$	$1$	$26.063$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(4\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}-2q^{7}+q^{9}+6q^{13}+\cdots\)
3264.2.a.bg	$3264$	$2$	3264.a	1.a	$1$	$2$	$2$	$26.063$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}+q^{9}+(-1+\beta )q^{11}+\cdots\)
3264.2.a.bh	$3264$	$2$	3264.a	1.a	$1$	$2$	$2$	$26.063$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}+2q^{7}+q^{9}+\beta q^{11}+\cdots\)
3264.2.a.bi	$3264$	$2$	3264.a	1.a	$1$	$2$	$2$	$26.063$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+(2-2\beta )q^{7}+q^{9}+(-4+\cdots)q^{11}+\cdots\)
3264.2.a.bj	$3264$	$2$	3264.a	1.a	$1$	$2$	$2$	$26.063$	\(\Q(\sqrt{57}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(8\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+4q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
3264.2.a.bk	$3264$	$2$	3264.a	1.a	$1$	$2$	$2$	$26.063$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(3\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+(2-2\beta )q^{7}+q^{9}+\cdots\)
3264.2.a.bl	$3264$	$2$	3264.a	1.a	$1$	$2$	$2$	$26.063$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+q^{9}+(1-\beta )q^{11}+\cdots\)
3264.2.a.bm	$3264$	$2$	3264.a	1.a	$1$	$2$	$2$	$26.063$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}-2q^{7}+q^{9}-\beta q^{11}+\cdots\)
3264.2.a.bn	$3264$	$2$	3264.a	1.a	$1$	$2$	$2$	$26.063$	\(\Q(\sqrt{57}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-8\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}-4q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
3264.2.a.bo	$3264$	$2$	3264.a	1.a	$1$	$2$	$2$	$26.063$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+(-2+2\beta )q^{7}+q^{9}+\cdots\)
3264.2.a.bp	$3264$	$2$	3264.a	1.a	$1$	$2$	$2$	$26.063$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(3\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+(-2+2\beta )q^{7}+q^{9}+\cdots\)
3264.2.a.bq	$3264$	$2$	3264.a	1.a	$1$	$3$	$3$	$26.063$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(2\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{1})q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
3264.2.a.br	$3264$	$2$	3264.a	1.a	$1$	$3$	$3$	$26.063$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-1\)	\(6\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+2q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
3264.2.a.bs	$3264$	$2$	3264.a	1.a	$1$	$3$	$3$	$26.063$	3.3.316.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(-3\)	\(-2\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{1})q^{5}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
3264.2.a.bt	$3264$	$2$	3264.a	1.a	$1$	$3$	$3$	$26.063$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(-1\)	\(-6\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}-2q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3264))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3264)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(408))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(544))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(816))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1088))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1632))\)\(^{\oplus 2}\)