Space of modular forms of level 19, weight 4, and trivial character

• Label: 19.4.a
• Level: $19$
• Weight: $4$
• Character orbit: 19.a
• Rep. character: $\chi_{19}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $6$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	19.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(6\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(19))\).

	Total	New	Old
Modular forms	6	4	2
Cusp forms	4	4	0
Eisenstein series	2	0	2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(19\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(4\)	\(3\)	\(1\)		\(3\)	\(3\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)		\(2\)	\(1\)	\(1\)		\(1\)	\(1\)	\(0\)		\(1\)	\(0\)	\(1\)

Trace form

4 * q - 4 * q^3 + 22 * q^4 + 2 * q^5 - 50 * q^6 - 24 * q^7 + 48 * q^8 + 46 * q^9 - 52 * q^10 - 38 * q^11 - 120 * q^12 + 76 * q^13 + 4 * q^14 + 200 * q^15 - 38 * q^16 - 64 * q^17 + 144 * q^18 - 38 * q^19 + 88 * q^20 - 80 * q^21 + 280 * q^22 + 82 * q^23 - 594 * q^24 - 18 * q^25 + 266 * q^26 - 232 * q^27 - 482 * q^28 + 128 * q^29 - 556 * q^30 - 84 * q^31 + 624 * q^32 + 140 * q^33 + 608 * q^34 - 570 * q^35 + 1072 * q^36 - 540 * q^37 - 114 * q^38 - 426 * q^39 - 324 * q^40 + 1196 * q^41 + 1550 * q^42 - 766 * q^43 + 56 * q^44 + 254 * q^45 - 788 * q^46 - 102 * q^47 - 1056 * q^48 - 320 * q^49 - 1696 * q^50 + 652 * q^51 + 708 * q^52 + 1252 * q^53 - 1382 * q^54 + 450 * q^55 - 684 * q^56 - 114 * q^57 + 1394 * q^58 + 460 * q^59 + 1420 * q^60 + 630 * q^61 - 1604 * q^62 - 1326 * q^63 + 274 * q^64 - 372 * q^65 - 1084 * q^66 - 1168 * q^67 - 1622 * q^68 - 108 * q^69 + 2436 * q^70 + 600 * q^71 + 2784 * q^72 + 980 * q^73 - 20 * q^74 + 1936 * q^75 - 380 * q^76 - 506 * q^77 - 1652 * q^78 + 348 * q^79 - 620 * q^80 - 1172 * q^81 + 152 * q^82 - 532 * q^83 + 852 * q^84 - 126 * q^85 + 3180 * q^86 - 426 * q^87 - 792 * q^88 - 340 * q^89 - 1960 * q^90 - 336 * q^91 - 2494 * q^92 + 612 * q^93 + 408 * q^94 - 494 * q^95 + 638 * q^96 - 1692 * q^97 - 1784 * q^98 + 358 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(19))\) 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					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		19
19.4.a.a	$19$	$4$	19.a	1.a	$1$	$1$	$1$	$1.121$	\(\Q\)	None	✓	✓	✓	✓	19.4.a.a	$1$	$1$	\(-3\)	\(-5\)	\(-12\)	\(11\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}-5q^{3}+q^{4}-12q^{5}+15q^{6}+\cdots\)
19.4.a.b	$19$	$4$	19.a	1.a	$1$	$3$	$3$	$1.121$	3.3.3144.1	None	✓	✓	✓	✓	19.4.a.b	$1$	$0$	\(3\)	\(1\)	\(14\)	\(-35\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1}-\beta _{2})q^{2}+(-\beta _{1}+2\beta _{2})q^{3}+\cdots\)