Space of modular forms of level 38, weight 2, and Character 38.c

• Label: 38.2.c
• Level: $38$
• Weight: $2$
• Character orbit: 38.c
• Rep. character: $\chi_{38}(7,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $10$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(10\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(38, [\chi])\).

	Total	New	Old
Modular forms	14	6	8
Cusp forms	6	6	0
Eisenstein series	8	0	8

Trace form

6 * q - q^2 - q^3 - 3 * q^4 - 2 * q^5 + q^6 - 4 * q^7 + 2 * q^8 - 6 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 - 6 * q^13 - 6 * q^14 + 14 * q^15 - 3 * q^16 + 6 * q^17 + 20 * q^18 + 5 * q^19 + 4 * q^20 - 10 * q^21 + 7 * q^22 + 4 * q^23 + q^24 - q^25 + 4 * q^26 - 10 * q^27 + 2 * q^28 + 2 * q^29 - 28 * q^30 - 8 * q^31 - q^32 + 11 * q^33 - 6 * q^34 + 12 * q^35 - 6 * q^36 - 8 * q^37 - 8 * q^38 + 4 * q^39 - 2 * q^40 - 19 * q^41 - 18 * q^42 - 8 * q^43 + q^44 + 16 * q^45 + 16 * q^46 - 14 * q^47 - q^48 + 22 * q^49 + 22 * q^50 + 6 * q^51 - 6 * q^52 - 2 * q^53 - 5 * q^54 - 10 * q^55 + 12 * q^56 + 36 * q^57 - 4 * q^58 + 9 * q^59 + 14 * q^60 + 18 * q^61 + 8 * q^62 - 16 * q^63 + 6 * q^64 + 8 * q^65 + 17 * q^66 + 11 * q^67 - 12 * q^68 - 40 * q^69 + 12 * q^70 + 22 * q^71 - 10 * q^72 - 13 * q^73 - 16 * q^74 - 66 * q^75 - 13 * q^76 - 60 * q^77 + 2 * q^78 + 12 * q^79 - 2 * q^80 + 9 * q^81 - q^82 + 6 * q^83 + 20 * q^84 - 16 * q^86 + 28 * q^87 - 14 * q^88 - 6 * q^89 - 8 * q^90 + 4 * q^91 + 4 * q^92 + 12 * q^93 + 28 * q^94 - 28 * q^95 - 2 * q^96 + q^97 + 7 * q^98 + 22 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(38, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
38.2.c.a	$38$	$2$	38.c	19.c	$3$	$2$	$1$	$0.303$	\(\Q(\sqrt{-3}) \)	None		✓			38.2.c.a	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
38.2.c.b	$38$	$2$	38.c	19.c	$3$	$4$	$2$	$0.303$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		✓	✓		38.2.c.b	$2$	$0$	\(-2\)	\(0\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)