Space of modular forms of level 38, weight 10, and Character 38.c

• Label: 38.10.c
• Level: $38$
• Weight: $10$
• Character orbit: 38.c
• Rep. character: $\chi_{38}(7,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $30$
• Newform subspaces: $2$
• Sturm bound: $50$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(50\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(38, [\chi])\).

	Total	New	Old
Modular forms	94	30	64
Cusp forms	86	30	56
Eisenstein series	8	0	8

Trace form

\( 30 q - 16 q^{2} + 235 q^{3} - 3840 q^{4} + 568 q^{5} - 1520 q^{6} + 7396 q^{7} + 8192 q^{8} - 105350 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(38, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
38.10.c.a	$38$	$10$	38.c	19.c	$3$	$14$	$7$	$19.571$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(112\)	\(165\)	\(909\)	\(3692\)	$2^{10}\cdot 3^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2^{4}-2^{4}\beta _{2})q^{2}+(24-\beta _{1}-24\beta _{2}+\cdots)q^{3}+\cdots\)
38.10.c.b	$38$	$10$	38.c	19.c	$3$	$16$	$8$	$19.571$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-128\)	\(70\)	\(-341\)	\(3704\)	$2^{12}\cdot 3^{5}\cdot 19^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2^{4}+2^{4}\beta _{2})q^{2}+(9-\beta _{1}-9\beta _{2}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(38, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)