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

• Label: 38.10.e
• Level: $38$
• Weight: $10$
• Character orbit: 38.e
• Rep. character: $\chi_{38}(5,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $90$
• Newform subspaces: $2$
• Sturm bound: $50$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
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	282	90	192
Cusp forms	258	90	168
Eisenstein series	24	0	24

Trace form

\( 90 q - 219 q^{3} + 4560 q^{6} - 11436 q^{7} - 12288 q^{8} + 20805 q^{9} + O(q^{10}) \)

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.e.a	$38$	$10$	38.e	19.e	$9$	$42$	$7$	$19.571$		None		$2$	$0$	\(0\)	\(-252\)	\(0\)	\(14373\)		$\mathrm{SU}(2)[C_{9}]$
38.10.e.b	$38$	$10$	38.e	19.e	$9$	$48$	$8$	$19.571$		None		$2$	$0$	\(0\)	\(33\)	\(0\)	\(-25809\)		$\mathrm{SU}(2)[C_{9}]$

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

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