Space of modular forms of level 29, weight 18, and trivial character

• Label: 29.18.a
• Level: $29$
• Weight: $18$
• Character orbit: 29.a
• Rep. character: $\chi_{29}(1,\cdot)$
• Character field: $\Q$
• Dimension: $39$
• Newform subspaces: $2$
• Sturm bound: $45$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(45\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(29))\).

	Total	New	Old
Modular forms	43	39	4
Cusp forms	41	39	2
Eisenstein series	2	0	2

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

\(29\)	Dim
\(+\)	\(18\)
\(-\)	\(21\)

Trace form

\( 39 q + 256 q^{2} + 8566 q^{3} + 2315220 q^{4} + 434044 q^{5} - 3254644 q^{6} - 41731672 q^{7} - 51200586 q^{8} + 1753365353 q^{9} + O(q^{10}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(29))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		29
29.18.a.a	$29$	$18$	29.a	1.a	$1$	$18$	$18$	$53.134$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-15400\)	\(-564228\)	\(-43925040\)		$+$	$+$	$2^{42}\cdot 3^{14}\cdot 17$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-856-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
29.18.a.b	$29$	$18$	29.a	1.a	$1$	$21$	$21$	$53.134$		None	✓	$1$	$0$	\(256\)	\(23966\)	\(998272\)	\(2193368\)		$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(29))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(29)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)