Space of modular forms of level 2645, weight 2, and trivial character

• Label: 2645.2.a
• Level: $2645$
• Weight: $2$
• Character orbit: 2645.a
• Rep. character: $\chi_{2645}(1,\cdot)$
• Character field: $\Q$
• Dimension: $169$
• Newform subspaces: $25$
• Sturm bound: $552$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2645 = 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2645.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 25 \)
Sturm bound:			\(552\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2645))\).

	Total	New	Old
Modular forms	300	169	131
Cusp forms	253	169	84
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.

\(5\)	\(23\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(37\)
\(+\)	\(-\)	$-$	\(48\)
\(-\)	\(+\)	$-$	\(47\)
\(-\)	\(-\)	$+$	\(37\)
Plus space		\(+\)	\(74\)
Minus space		\(-\)	\(95\)

Trace form

\( 169 q - q^{2} + 4 q^{3} + 167 q^{4} - q^{5} - 8 q^{6} + 4 q^{7} - 9 q^{8} + 177 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2645))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	23
2645.2.a.a	$2645$	$2$	2645.a	1.a	$1$	$1$	$1$	$21.120$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{4}-q^{5}+3q^{7}+q^{9}+6q^{11}+\cdots\)
2645.2.a.b	$2645$	$2$	2645.a	1.a	$1$	$1$	$1$	$21.120$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{4}+q^{5}-3q^{7}+q^{9}-6q^{11}+\cdots\)
2645.2.a.c	$2645$	$2$	2645.a	1.a	$1$	$1$	$1$	$21.120$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{5}-q^{7}-3q^{9}+2q^{10}+\cdots\)
2645.2.a.d	$2645$	$2$	2645.a	1.a	$1$	$2$	$2$	$21.120$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-3\)	\(-2\)	\(2\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+q^{5}+\cdots\)
2645.2.a.e	$2645$	$2$	2645.a	1.a	$1$	$2$	$2$	$21.120$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(-2\)	\(2\)	\(-2\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(2-2\beta )q^{4}+\cdots\)
2645.2.a.f	$2645$	$2$	2645.a	1.a	$1$	$2$	$2$	$21.120$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(-2\)	\(2\)	\(2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(2-2\beta )q^{4}+\cdots\)
2645.2.a.g	$2645$	$2$	2645.a	1.a	$1$	$2$	$2$	$21.120$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(-1\)	\(2\)	\(-2\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
2645.2.a.h	$2645$	$2$	2645.a	1.a	$1$	$2$	$2$	$21.120$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(-1\)	\(2\)	\(2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(1+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots\)
2645.2.a.i	$2645$	$2$	2645.a	1.a	$1$	$4$	$4$	$21.120$	4.4.65057.1	None	✓	$1$	$0$	\(-1\)	\(-1\)	\(-4\)	\(7\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
2645.2.a.j	$2645$	$2$	2645.a	1.a	$1$	$4$	$4$	$21.120$	4.4.65057.1	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(4\)	\(-7\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(2+\beta _{2})q^{4}+q^{5}+\cdots\)
2645.2.a.k	$2645$	$2$	2645.a	1.a	$1$	$4$	$4$	$21.120$	4.4.2777.1	None	✓	$1$	$0$	\(-1\)	\(1\)	\(-4\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
2645.2.a.l	$2645$	$2$	2645.a	1.a	$1$	$4$	$4$	$21.120$	4.4.2777.1	None	✓	$1$	$1$	\(-1\)	\(1\)	\(4\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
2645.2.a.m	$2645$	$2$	2645.a	1.a	$1$	$4$	$4$	$21.120$	4.4.15317.1	None	✓	$1$	$0$	\(2\)	\(-2\)	\(-4\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2645.2.a.n	$2645$	$2$	2645.a	1.a	$1$	$5$	$5$	$21.120$	\(\Q(\zeta_{22})^+\)	None	✓	$1$	$1$	\(-3\)	\(-5\)	\(-5\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}-\beta _{4})q^{2}-q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
2645.2.a.o	$2645$	$2$	2645.a	1.a	$1$	$5$	$5$	$21.120$	\(\Q(\zeta_{22})^+\)	None	✓	$1$	$1$	\(-3\)	\(-5\)	\(5\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}-\beta _{4})q^{2}-q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
2645.2.a.p	$2645$	$2$	2645.a	1.a	$1$	$6$	$6$	$21.120$	6.6.27387072.1	None	✓	$1$	$0$	\(0\)	\(-6\)	\(-6\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(1+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
2645.2.a.q	$2645$	$2$	2645.a	1.a	$1$	$6$	$6$	$21.120$	6.6.27387072.1	None	✓	$1$	$1$	\(0\)	\(-6\)	\(6\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(1+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
2645.2.a.r	$2645$	$2$	2645.a	1.a	$1$	$6$	$6$	$21.120$	6.6.4829696.1	None	✓	$1$	$1$	\(2\)	\(4\)	\(-6\)	\(-6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
2645.2.a.s	$2645$	$2$	2645.a	1.a	$1$	$6$	$6$	$21.120$	6.6.4829696.1	None	✓	$1$	$0$	\(2\)	\(4\)	\(6\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
2645.2.a.t	$2645$	$2$	2645.a	1.a	$1$	$10$	$10$	$21.120$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(-5\)	\(-10\)	\(9\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}-\beta _{1}q^{3}-\beta _{7}q^{4}-q^{5}+\beta _{3}q^{6}+\cdots\)
2645.2.a.u	$2645$	$2$	2645.a	1.a	$1$	$10$	$10$	$21.120$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(-5\)	\(10\)	\(-9\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(-1+\beta _{1})q^{3}-\beta _{7}q^{4}+q^{5}+\cdots\)
2645.2.a.v	$2645$	$2$	2645.a	1.a	$1$	$16$	$16$	$21.120$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$1$	\(4\)	\(4\)	\(-16\)	\(-12\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
2645.2.a.w	$2645$	$2$	2645.a	1.a	$1$	$16$	$16$	$21.120$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(4\)	\(16\)	\(12\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
2645.2.a.x	$2645$	$2$	2645.a	1.a	$1$	$25$	$25$	$21.120$		None	✓	$1$	$0$	\(3\)	\(10\)	\(-25\)	\(-14\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
2645.2.a.y	$2645$	$2$	2645.a	1.a	$1$	$25$	$25$	$21.120$		None	✓	$1$	$0$	\(3\)	\(10\)	\(25\)	\(14\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2645))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2645)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 2}\)