Space of modular forms of level 4028, weight 2, and trivial character

• Label: 4028.2.a
• Level: $4028$
• Weight: $2$
• Character orbit: 4028.a
• Rep. character: $\chi_{4028}(1,\cdot)$
• Character field: $\Q$
• Dimension: $78$
• Newform subspaces: $6$
• Sturm bound: $1080$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4028.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1080\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4028))\).

	Total	New	Old
Modular forms	546	78	468
Cusp forms	535	78	457
Eisenstein series	11	0	11

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

\(2\)	\(19\)	\(53\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	$-$	\(19\)
\(-\)	\(+\)	\(-\)	$+$	\(19\)
\(-\)	\(-\)	\(+\)	$+$	\(20\)
\(-\)	\(-\)	\(-\)	$-$	\(20\)
Plus space			\(+\)	\(39\)
Minus space			\(-\)	\(39\)

Trace form

\( 78 q + 2 q^{5} - 2 q^{7} + 78 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4028))\) 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	19	53
4028.2.a.a	$4028$	$2$	4028.a	1.a	$1$	$1$	$1$	$32.164$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}-2q^{9}+q^{11}-6q^{13}+\cdots\)
4028.2.a.b	$4028$	$2$	4028.a	1.a	$1$	$1$	$1$	$32.164$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-4q^{7}-2q^{9}-3q^{11}+\cdots\)
4028.2.a.c	$4028$	$2$	4028.a	1.a	$1$	$19$	$19$	$32.164$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-5\)	\(-5\)	\(-10\)		$-$	$-$	$+$	$+$	$3^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{10}q^{5}+(-1+\beta _{8})q^{7}+\cdots\)
4028.2.a.d	$4028$	$2$	4028.a	1.a	$1$	$19$	$19$	$32.164$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-2\)	\(-11\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{6}q^{5}+(-1+\beta _{11})q^{7}+\cdots\)
4028.2.a.e	$4028$	$2$	4028.a	1.a	$1$	$19$	$19$	$32.164$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(3\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}-\beta _{18}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
4028.2.a.f	$4028$	$2$	4028.a	1.a	$1$	$19$	$19$	$32.164$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(4\)	\(4\)	\(13\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{7}q^{5}+(1+\beta _{8})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4028))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4028)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(106))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(212))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1007))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2014))\)\(^{\oplus 2}\)