Space of modular forms of level 38, weight 4, and Character 38.c

• Label: 38.4.c
• Level: $38$
• Weight: $4$
• Character orbit: 38.c
• Rep. character: $\chi_{38}(7,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $10$
• Newform subspaces: $3$
• Sturm bound: $20$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(20\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(38, [\chi])\).

	Total	New	Old
Modular forms	34	10	24
Cusp forms	26	10	16
Eisenstein series	8	0	8

Trace form

10 * q + 2 * q^2 - 5 * q^3 - 20 * q^4 + 8 * q^5 + 10 * q^6 + 4 * q^7 - 16 * q^8 - 50 * q^9 + 20 * q^10 + 34 * q^11 + 40 * q^12 + 172 * q^13 + 100 * q^14 - 152 * q^15 - 80 * q^16 - 184 * q^17 - 232 * q^18 + 59 * q^19 - 64 * q^20 + 30 * q^21 - 18 * q^22 + 58 * q^23 + 40 * q^24 - 241 * q^25 + 344 * q^26 + 718 * q^27 - 8 * q^28 + 28 * q^29 - 8 * q^30 - 168 * q^31 + 32 * q^32 + 299 * q^33 - 164 * q^34 + 108 * q^35 - 200 * q^36 - 1072 * q^37 + 360 * q^38 - 2496 * q^39 + 80 * q^40 + 711 * q^41 + 740 * q^42 + 114 * q^43 - 68 * q^44 + 3224 * q^45 + 144 * q^46 + 868 * q^47 - 80 * q^48 - 550 * q^49 - 1740 * q^50 + 544 * q^51 + 688 * q^52 - 1032 * q^53 + 718 * q^54 - 1742 * q^55 - 800 * q^56 + 330 * q^57 - 1112 * q^58 + 113 * q^59 - 608 * q^60 - 412 * q^61 - 32 * q^62 - 920 * q^63 + 640 * q^64 - 452 * q^65 - 498 * q^66 + 347 * q^67 + 1472 * q^68 - 76 * q^69 + 552 * q^70 + 1428 * q^71 + 464 * q^72 - 203 * q^73 + 320 * q^74 + 3234 * q^75 + 332 * q^76 - 604 * q^77 - 596 * q^78 + 1638 * q^79 + 128 * q^80 + 55 * q^81 - 478 * q^82 - 1142 * q^83 - 240 * q^84 - 618 * q^85 + 520 * q^86 - 3880 * q^87 + 144 * q^88 + 2156 * q^89 + 3152 * q^90 - 740 * q^91 + 232 * q^92 - 1988 * q^93 - 5400 * q^94 + 2266 * q^95 - 320 * q^96 + 571 * q^97 - 2158 * q^98 - 3158 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(38, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
38.4.c.a	$38$	$4$	38.c	19.c	$3$	$2$	$1$	$2.242$	\(\Q(\sqrt{-3}) \)	None		✓			38.4.c.a	$2$	$0$	\(-2\)	\(-5\)	\(-3\)	\(-64\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}+(-5+5\zeta_{6})q^{3}+\cdots\)
38.4.c.b	$38$	$4$	38.c	19.c	$3$	$2$	$1$	$2.242$	\(\Q(\sqrt{-3}) \)	None		✓			38.4.c.b	$2$	$0$	\(-2\)	\(5\)	\(12\)	\(16\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}+(5-5\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
38.4.c.c	$38$	$4$	38.c	19.c	$3$	$6$	$3$	$2.242$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		✓	✓		38.4.c.c	$2$	$0$	\(6\)	\(-5\)	\(-1\)	\(52\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\beta _{4})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{4}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(38, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(38, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)