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

• Label: 38.4.e
• Level: $38$
• Weight: $4$
• Character orbit: 38.e
• Rep. character: $\chi_{38}(5,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $30$
• Newform subspaces: $2$
• Sturm bound: $20$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(20\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	102	30	72
Cusp forms	78	30	48
Eisenstein series	24	0	24

Trace form

30 * q - 3 * q^3 - 30 * q^6 - 12 * q^7 + 24 * q^8 + 15 * q^9 - 84 * q^11 + 72 * q^12 + 138 * q^13 + 24 * q^14 + 240 * q^15 - 42 * q^17 - 276 * q^18 - 834 * q^19 - 192 * q^20 - 486 * q^21 + 24 * q^22 + 132 * q^23 - 120 * q^24 + 876 * q^25 + 228 * q^26 + 867 * q^27 + 408 * q^28 + 828 * q^29 + 30 * q^31 - 1245 * q^33 + 360 * q^34 - 2130 * q^35 + 60 * q^36 + 60 * q^37 - 474 * q^38 + 564 * q^39 - 63 * q^41 + 72 * q^42 - 516 * q^43 + 768 * q^44 + 2790 * q^45 + 1200 * q^46 + 1932 * q^47 + 96 * q^48 + 555 * q^49 + 714 * q^50 + 345 * q^51 - 816 * q^52 - 882 * q^53 - 3438 * q^54 - 1296 * q^55 - 864 * q^56 - 5484 * q^57 - 1296 * q^58 - 4197 * q^59 + 240 * q^60 - 990 * q^61 - 1764 * q^62 + 1578 * q^63 - 960 * q^64 + 2250 * q^65 + 3162 * q^66 + 2385 * q^67 - 540 * q^68 + 3456 * q^69 + 3720 * q^70 + 4650 * q^71 + 1104 * q^72 - 378 * q^73 - 396 * q^74 - 6300 * q^75 - 408 * q^76 + 4404 * q^77 + 4884 * q^78 + 216 * q^79 + 5205 * q^81 + 714 * q^82 + 1308 * q^83 + 1296 * q^84 - 2028 * q^85 - 2208 * q^86 - 1614 * q^87 + 528 * q^88 - 1980 * q^89 - 7224 * q^90 - 516 * q^91 - 2784 * q^92 - 7734 * q^93 + 168 * q^94 + 1434 * q^95 - 453 * q^97 - 576 * q^98 - 561 * 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.e.a	$38$	$4$	38.e	19.e	$9$	$12$	$2$	$2.242$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			38.4.e.a	$2$	$0$	\(0\)	\(-9\)	\(0\)	\(21\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-2\beta _{3}q^{2}+(-1+2\beta _{2}-\beta _{4}+2\beta _{6}+\cdots)q^{3}+\cdots\)
38.4.e.b	$38$	$4$	38.e	19.e	$9$	$18$	$3$	$2.242$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		✓	✓		38.4.e.b	$2$	$0$	\(0\)	\(6\)	\(0\)	\(-33\)	$3^{2}$	$\mathrm{SU}(2)[C_{9}]$	\(q-2\beta _{8}q^{2}+(\beta _{3}+\beta _{4}+\beta _{6}+\beta _{9})q^{3}+\cdots\)

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

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