Space of modular forms of level 4901, weight 2, and trivial character

• Label: 4901.2.a
• Level: $4901$
• Weight: $2$
• Character orbit: 4901.a
• Rep. character: $\chi_{4901}(1,\cdot)$
• Character field: $\Q$
• Dimension: $361$
• Newform subspaces: $24$
• Sturm bound: $910$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 4901 = 13^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4901.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 24 \)
Sturm bound:			\(910\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4901))\).

	Total	New	Old
Modular forms	468	361	107
Cusp forms	441	361	80
Eisenstein series	27	0	27

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

\(13\)	\(29\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(82\)
\(+\)	\(-\)	$-$	\(97\)
\(-\)	\(+\)	$-$	\(100\)
\(-\)	\(-\)	$+$	\(82\)
Plus space		\(+\)	\(164\)
Minus space		\(-\)	\(197\)

Trace form

\( 361 q + q^{2} + 2 q^{3} + 363 q^{4} + 4 q^{5} + 6 q^{6} - 4 q^{7} + 9 q^{8} + 367 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4901))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		13	29
4901.2.a.a	$4901$	$2$	4901.a	1.a	$1$	$1$	$1$	$39.135$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(2\)	\(3\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{3}+2q^{4}+3q^{5}-4q^{6}+\cdots\)
4901.2.a.b	$4901$	$2$	4901.a	1.a	$1$	$1$	$1$	$39.135$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}+3q^{8}-3q^{9}-2q^{10}+\cdots\)
4901.2.a.c	$4901$	$2$	4901.a	1.a	$1$	$1$	$1$	$39.135$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(2\)	\(-3\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{3}+2q^{4}-3q^{5}+4q^{6}+\cdots\)
4901.2.a.d	$4901$	$2$	4901.a	1.a	$1$	$2$	$2$	$39.135$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+q^{4}+\beta q^{5}-\beta q^{6}-\beta q^{8}+\cdots\)
4901.2.a.e	$4901$	$2$	4901.a	1.a	$1$	$2$	$2$	$39.135$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1-\beta )q^{3}+q^{4}-2\beta q^{5}+(-3+\cdots)q^{6}+\cdots\)
4901.2.a.f	$4901$	$2$	4901.a	1.a	$1$	$2$	$2$	$39.135$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$1$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+2q^{3}+q^{4}+2\beta q^{6}-\beta q^{8}+\cdots\)
4901.2.a.g	$4901$	$2$	4901.a	1.a	$1$	$2$	$2$	$39.135$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+\beta )q^{3}+(1+2\beta )q^{4}+\cdots\)
4901.2.a.h	$4901$	$2$	4901.a	1.a	$1$	$4$	$4$	$39.135$	\(\Q(\zeta_{24})^+\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+q^{4}+2\beta _{2}q^{5}+3\beta _{2}q^{6}+\cdots\)
4901.2.a.i	$4901$	$2$	4901.a	1.a	$1$	$5$	$5$	$39.135$	5.5.36497.1	None	✓	$1$	$1$	\(1\)	\(-4\)	\(2\)	\(11\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(-1-\beta _{4})q^{3}+(\beta _{1}+\beta _{4})q^{4}+\cdots\)
4901.2.a.j	$4901$	$2$	4901.a	1.a	$1$	$5$	$5$	$39.135$	5.5.202817.1	None	✓	$1$	$0$	\(3\)	\(-4\)	\(-2\)	\(15\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{4})q^{2}+(-1-\beta _{3})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
4901.2.a.k	$4901$	$2$	4901.a	1.a	$1$	$7$	$7$	$39.135$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(-3\)	\(2\)	\(2\)	\(-7\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{6}q^{2}+\beta _{2}q^{3}+(2-\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
4901.2.a.l	$4901$	$2$	4901.a	1.a	$1$	$9$	$9$	$39.135$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(-17\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
4901.2.a.m	$4901$	$2$	4901.a	1.a	$1$	$12$	$12$	$39.135$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(-7\)	\(3\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(\beta _{1}+\beta _{4}+\cdots)q^{4}+\cdots\)
4901.2.a.n	$4901$	$2$	4901.a	1.a	$1$	$12$	$12$	$39.135$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(-12\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4901.2.a.o	$4901$	$2$	4901.a	1.a	$1$	$12$	$12$	$39.135$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(2\)	\(-7\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(\beta _{1}+\beta _{4}+\cdots)q^{4}+\cdots\)
4901.2.a.p	$4901$	$2$	4901.a	1.a	$1$	$14$	$14$	$39.135$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(2+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots\)
4901.2.a.q	$4901$	$2$	4901.a	1.a	$1$	$19$	$19$	$39.135$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(7\)	\(0\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
4901.2.a.r	$4901$	$2$	4901.a	1.a	$1$	$19$	$19$	$39.135$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(7\)	\(0\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots\)
4901.2.a.s	$4901$	$2$	4901.a	1.a	$1$	$26$	$26$	$39.135$		None	✓	$2$	$1$	\(0\)	\(-14\)	\(0\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
4901.2.a.t	$4901$	$2$	4901.a	1.a	$1$	$38$	$38$	$39.135$		None	✓	$2$	$0$	\(0\)	\(10\)	\(0\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
4901.2.a.u	$4901$	$2$	4901.a	1.a	$1$	$42$	$42$	$39.135$		None	✓	$1$	$1$	\(-6\)	\(2\)	\(-10\)	\(-23\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
4901.2.a.v	$4901$	$2$	4901.a	1.a	$1$	$42$	$42$	$39.135$		None	✓	$1$	$1$	\(0\)	\(2\)	\(-14\)	\(-25\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
4901.2.a.w	$4901$	$2$	4901.a	1.a	$1$	$42$	$42$	$39.135$		None	✓	$1$	$0$	\(0\)	\(2\)	\(14\)	\(25\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
4901.2.a.x	$4901$	$2$	4901.a	1.a	$1$	$42$	$42$	$39.135$		None	✓	$1$	$0$	\(6\)	\(2\)	\(10\)	\(23\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4901))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4901)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(377))\)\(^{\oplus 2}\)