Space of modular forms of level 16, weight 18, and trivial character

• Label: 16.18.a
• Level: $16$
• Weight: $18$
• Character orbit: 16.a
• Rep. character: $\chi_{16}(1,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $5$
• Sturm bound: $36$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	16.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(36\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(16))\).

	Total	New	Old
Modular forms	37	9	28
Cusp forms	31	8	23
Eisenstein series	6	1	5

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

\(2\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(18\)	\(4\)	\(14\)		\(15\)	\(4\)	\(11\)		\(3\)	\(0\)	\(3\)
\(-\)		\(19\)	\(5\)	\(14\)		\(16\)	\(4\)	\(12\)		\(3\)	\(1\)	\(2\)

Trace form

8 * q - 6560 * q^3 - 12240 * q^5 + 13155520 * q^7 + 381202024 * q^9 - 638633184 * q^11 - 795138960 * q^13 + 22854157888 * q^15 + 9464779920 * q^17 - 122492026912 * q^19 - 128236029696 * q^21 - 169801828800 * q^23 + 327793560312 * q^25 + 2437057593280 * q^27 + 322615944432 * q^29 - 2348232551680 * q^31 - 195602811520 * q^33 - 17952557683584 * q^35 - 4030094403280 * q^37 + 40546924882240 * q^39 - 9753146876592 * q^41 + 38935793294880 * q^43 - 19570686122384 * q^45 - 217219263484800 * q^47 + 424502305947080 * q^49 + 187754960315072 * q^51 - 728845213949520 * q^53 + 453009721885376 * q^55 - 1096531773403520 * q^57 - 1838057785645152 * q^59 + 2554878729448944 * q^61 + 1874994489746880 * q^63 + 3757237690743456 * q^65 + 3140248986451040 * q^67 - 7229964229776640 * q^69 - 6110717387570496 * q^71 - 9399120337579440 * q^73 - 6730097528054368 * q^75 + 14016035510496000 * q^77 + 23979939181199232 * q^79 + 10259622068861896 * q^81 - 35643037465758240 * q^83 + 1402722648726368 * q^85 + 57285930233352000 * q^87 - 17574490465707312 * q^89 - 63745031209815424 * q^91 - 9523538651356160 * q^93 + 77139367155523392 * q^95 - 71510264285450480 * q^97 - 158650192815441760 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(16))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2
16.18.a.a	$16$	$18$	16.a	1.a	$1$	$1$	$1$	$29.316$	\(\Q\)	None	✓				2.18.a.a	$1$	$0$	\(0\)	\(-6084\)	\(1255110\)	\(22465912\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-78^{2}q^{3}+1255110q^{5}+22465912q^{7}+\cdots\)
16.18.a.b	$16$	$18$	16.a	1.a	$1$	$1$	$1$	$29.316$	\(\Q\)	None	✓				1.18.a.a	$1$	$0$	\(0\)	\(4284\)	\(-1025850\)	\(-3225992\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4284q^{3}-1025850q^{5}-3225992q^{7}+\cdots\)
16.18.a.c	$16$	$18$	16.a	1.a	$1$	$2$	$2$	$29.316$	\(\Q(\sqrt{114}) \)	None	✓				8.18.a.b	$1$	$1$	\(0\)	\(-11592\)	\(-791924\)	\(18932592\)		$+$	$+$	$2^{7}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-5796+\beta )q^{3}+(-395962+68\beta )q^{5}+\cdots\)
16.18.a.d	$16$	$18$	16.a	1.a	$1$	$2$	$2$	$29.316$	\(\Q(\sqrt{2146}) \)	None	✓				8.18.a.a	$1$	$1$	\(0\)	\(952\)	\(-53620\)	\(333168\)		$+$	$+$	$2^{8}$	$\mathrm{SU}(2)$	\(q+(476+\beta )q^{3}+(-26810-60\beta )q^{5}+\cdots\)
16.18.a.e	$16$	$18$	16.a	1.a	$1$	$2$	$2$	$29.316$	\(\Q(\sqrt{9361}) \)	None	✓		✓		4.18.a.a	$1$	$0$	\(0\)	\(5880\)	\(604044\)	\(-25350160\)		$-$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(2940-\beta )q^{3}+(302022-6^{2}\beta )q^{5}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(16)) \simeq \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)