Space of modular forms of level 4017, weight 2, and trivial character

• Label: 4017.2.a
• Level: $4017$
• Weight: $2$
• Character orbit: 4017.a
• Rep. character: $\chi_{4017}(1,\cdot)$
• Character field: $\Q$
• Dimension: $203$
• Newform subspaces: $12$
• Sturm bound: $970$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(970\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4017))\).

	Total	New	Old
Modular forms	488	203	285
Cusp forms	481	203	278
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.

\(3\)	\(13\)	\(103\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(26\)
\(+\)	\(+\)	\(-\)	$-$	\(24\)
\(+\)	\(-\)	\(+\)	$-$	\(25\)
\(+\)	\(-\)	\(-\)	$+$	\(27\)
\(-\)	\(+\)	\(+\)	$-$	\(32\)
\(-\)	\(+\)	\(-\)	$+$	\(18\)
\(-\)	\(-\)	\(+\)	$+$	\(19\)
\(-\)	\(-\)	\(-\)	$-$	\(32\)
Plus space			\(+\)	\(90\)
Minus space			\(-\)	\(113\)

Trace form

\( 203 q + 5 q^{2} - q^{3} + 213 q^{4} + 2 q^{5} + 5 q^{6} + 8 q^{7} + 9 q^{8} + 203 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4017))\) 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	13	103
4017.2.a.a	$4017$	$2$	4017.a	1.a	$1$	$1$	$1$	$32.076$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots\)
4017.2.a.b	$4017$	$2$	4017.a	1.a	$1$	$1$	$1$	$32.076$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}-2q^{7}+\cdots\)
4017.2.a.c	$4017$	$2$	4017.a	1.a	$1$	$1$	$1$	$32.076$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{5}+2q^{7}+q^{9}-2q^{12}+\cdots\)
4017.2.a.d	$4017$	$2$	4017.a	1.a	$1$	$2$	$2$	$32.076$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(-2\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
4017.2.a.e	$4017$	$2$	4017.a	1.a	$1$	$16$	$16$	$32.076$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(16\)	\(-6\)	\(-13\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots\)
4017.2.a.f	$4017$	$2$	4017.a	1.a	$1$	$19$	$19$	$32.076$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$1$	\(-4\)	\(19\)	\(-3\)	\(-23\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{16}q^{5}+\cdots\)
4017.2.a.g	$4017$	$2$	4017.a	1.a	$1$	$24$	$24$	$32.076$		None	✓	$1$	$0$	\(3\)	\(-24\)	\(3\)	\(11\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
4017.2.a.h	$4017$	$2$	4017.a	1.a	$1$	$25$	$25$	$32.076$		None	✓	$1$	$1$	\(-4\)	\(-25\)	\(-5\)	\(-7\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
4017.2.a.i	$4017$	$2$	4017.a	1.a	$1$	$25$	$25$	$32.076$		None	✓	$1$	$1$	\(-2\)	\(-25\)	\(-3\)	\(-11\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
4017.2.a.j	$4017$	$2$	4017.a	1.a	$1$	$25$	$25$	$32.076$		None	✓	$1$	$0$	\(6\)	\(-25\)	\(7\)	\(17\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
4017.2.a.k	$4017$	$2$	4017.a	1.a	$1$	$32$	$32$	$32.076$		None	✓	$1$	$0$	\(5\)	\(32\)	\(7\)	\(25\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
4017.2.a.l	$4017$	$2$	4017.a	1.a	$1$	$32$	$32$	$32.076$		None	✓	$1$	$0$	\(5\)	\(32\)	\(1\)	\(11\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4017))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4017)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(103))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(309))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1339))\)\(^{\oplus 2}\)