Space of modular forms of level 4029, weight 2, and trivial character

• Label: 4029.2.a
• Level: $4029$
• Weight: $2$
• Character orbit: 4029.a
• Rep. character: $\chi_{4029}(1,\cdot)$
• Character field: $\Q$
• Dimension: $207$
• Newform subspaces: $12$
• Sturm bound: $960$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(960\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4029))\).

	Total	New	Old
Modular forms	484	207	277
Cusp forms	477	207	270
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.

\(3\)	\(17\)	\(79\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(22\)
\(+\)	\(+\)	\(-\)	$-$	\(32\)
\(+\)	\(-\)	\(+\)	$-$	\(25\)
\(+\)	\(-\)	\(-\)	$+$	\(25\)
\(-\)	\(+\)	\(+\)	$-$	\(25\)
\(-\)	\(+\)	\(-\)	$+$	\(25\)
\(-\)	\(-\)	\(+\)	$+$	\(22\)
\(-\)	\(-\)	\(-\)	$-$	\(31\)
Plus space			\(+\)	\(94\)
Minus space			\(-\)	\(113\)

Trace form

\( 207 q - 3 q^{2} - q^{3} + 201 q^{4} - 6 q^{5} - 3 q^{6} - 8 q^{7} + 9 q^{8} + 207 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4029))\) 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	17	79
4029.2.a.a	$4029$	$2$	4029.a	1.a	$1$	$1$	$1$	$32.172$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}-4q^{11}+\cdots\)
4029.2.a.b	$4029$	$2$	4029.a	1.a	$1$	$1$	$1$	$32.172$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{5}-2q^{7}+q^{9}+3q^{11}+\cdots\)
4029.2.a.c	$4029$	$2$	4029.a	1.a	$1$	$2$	$2$	$32.172$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+(-1+\beta )q^{5}+\beta q^{6}+\cdots\)
4029.2.a.d	$4029$	$2$	4029.a	1.a	$1$	$3$	$3$	$32.172$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
4029.2.a.e	$4029$	$2$	4029.a	1.a	$1$	$18$	$18$	$32.172$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$1$	$1$	\(-6\)	\(18\)	\(-5\)	\(-13\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{14}q^{5}+\cdots\)
4029.2.a.f	$4029$	$2$	4029.a	1.a	$1$	$22$	$22$	$32.172$		None	✓	$1$	$1$	\(1\)	\(-22\)	\(1\)	\(-15\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
4029.2.a.g	$4029$	$2$	4029.a	1.a	$1$	$22$	$22$	$32.172$		None	✓	$1$	$1$	\(2\)	\(-22\)	\(5\)	\(-4\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
4029.2.a.h	$4029$	$2$	4029.a	1.a	$1$	$25$	$25$	$32.172$		None	✓	$1$	$1$	\(-7\)	\(25\)	\(-12\)	\(-4\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
4029.2.a.i	$4029$	$2$	4029.a	1.a	$1$	$25$	$25$	$32.172$		None	✓	$1$	$0$	\(-2\)	\(-25\)	\(-2\)	\(12\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
4029.2.a.j	$4029$	$2$	4029.a	1.a	$1$	$25$	$25$	$32.172$		None	✓	$1$	$0$	\(6\)	\(25\)	\(6\)	\(4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
4029.2.a.k	$4029$	$2$	4029.a	1.a	$1$	$31$	$31$	$32.172$		None	✓	$1$	$0$	\(4\)	\(31\)	\(11\)	\(4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
4029.2.a.l	$4029$	$2$	4029.a	1.a	$1$	$32$	$32$	$32.172$		None	✓	$1$	$0$	\(-1\)	\(-32\)	\(-1\)	\(4\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4029))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4029)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(79))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(237))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1343))\)\(^{\oplus 2}\)