Space of modular forms of level 3021, weight 2, and trivial character

• Label: 3021.2.a
• Level: $3021$
• Weight: $2$
• Character orbit: 3021.a
• Rep. character: $\chi_{3021}(1,\cdot)$
• Character field: $\Q$
• Dimension: $155$
• Newform subspaces: $11$
• Sturm bound: $720$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 3021 = 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3021.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(720\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3021))\).

	Total	New	Old
Modular forms	364	155	209
Cusp forms	357	155	202
Eisenstein series	7	0	7

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

\(3\)	\(19\)	\(53\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(19\)
\(+\)	\(+\)	\(-\)	$-$	\(18\)
\(+\)	\(-\)	\(+\)	$-$	\(25\)
\(+\)	\(-\)	\(-\)	$+$	\(16\)
\(-\)	\(+\)	\(+\)	$-$	\(18\)
\(-\)	\(+\)	\(-\)	$+$	\(19\)
\(-\)	\(-\)	\(+\)	$+$	\(16\)
\(-\)	\(-\)	\(-\)	$-$	\(24\)
Plus space			\(+\)	\(70\)
Minus space			\(-\)	\(85\)

Trace form

\( 155 q - 3 q^{2} - q^{3} + 149 q^{4} - 2 q^{5} - 3 q^{6} - 4 q^{7} - 15 q^{8} + 155 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3021))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	19	53
3021.2.a.a	$3021$	$2$	3021.a	1.a	$1$	$1$	$1$	$24.123$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(1\)	\(1\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots\)
3021.2.a.b	$3021$	$2$	3021.a	1.a	$1$	$1$	$1$	$24.123$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+4q^{5}+q^{6}-3q^{8}+\cdots\)
3021.2.a.c	$3021$	$2$	3021.a	1.a	$1$	$2$	$2$	$24.123$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(2\)	\(2\)	\(6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots\)
3021.2.a.d	$3021$	$2$	3021.a	1.a	$1$	$14$	$14$	$24.123$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(14\)	\(3\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots\)
3021.2.a.e	$3021$	$2$	3021.a	1.a	$1$	$16$	$16$	$24.123$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$1$	\(-7\)	\(16\)	\(-13\)	\(-8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
3021.2.a.f	$3021$	$2$	3021.a	1.a	$1$	$16$	$16$	$24.123$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$1$	\(3\)	\(-16\)	\(-5\)	\(-8\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{14}q^{5}+\cdots\)
3021.2.a.g	$3021$	$2$	3021.a	1.a	$1$	$18$	$18$	$24.123$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-18\)	\(2\)	\(5\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots\)
3021.2.a.h	$3021$	$2$	3021.a	1.a	$1$	$19$	$19$	$24.123$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$1$	\(-6\)	\(19\)	\(-14\)	\(-7\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{9}+\cdots)q^{5}+\cdots\)
3021.2.a.i	$3021$	$2$	3021.a	1.a	$1$	$19$	$19$	$24.123$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$1$	\(2\)	\(-19\)	\(2\)	\(-7\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots\)
3021.2.a.j	$3021$	$2$	3021.a	1.a	$1$	$24$	$24$	$24.123$		None	✓	$1$	$0$	\(6\)	\(24\)	\(13\)	\(4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
3021.2.a.k	$3021$	$2$	3021.a	1.a	$1$	$25$	$25$	$24.123$		None	✓	$1$	$0$	\(-5\)	\(-25\)	\(3\)	\(12\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3021))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3021)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(159))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1007))\)\(^{\oplus 2}\)