Space of modular forms of level 16, weight 26, and trivial character

• Label: 16.26.a
• Level: $16$
• Weight: $26$
• Character orbit: 16.a
• Rep. character: $\chi_{16}(1,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $6$
• Sturm bound: $52$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	16.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(52\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(16))\).

	Total	New	Old
Modular forms	53	13	40
Cusp forms	47	12	35
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.

\(2\)	Dim
\(+\)	\(6\)
\(-\)	\(6\)

Trace form

12 * q - 531440 * q^3 + 153134280 * q^5 + 49570129440 * q^7 + 2747998934812 * q^9 - 16415673834960 * q^11 + 35520940152360 * q^13 - 231131385901472 * q^15 - 508652996207400 * q^17 + 9218549184249936 * q^19 + 21359095797814656 * q^21 + 171058373102590560 * q^23 + 742154438320879092 * q^25 - 67457633233044320 * q^27 - 1032254880229804824 * q^29 + 10611514763327961216 * q^31 + 6200363844091350080 * q^33 - 61325131336226697024 * q^35 - 47048246844394209720 * q^37 + 44592267118282562272 * q^39 - 79427185216773458184 * q^41 + 63741600747917484720 * q^43 - 19819387223345474264 * q^45 - 672176079947849659200 * q^47 + 3043282679214606669228 * q^49 + 5577266654770934774048 * q^51 - 3472213210012668647160 * q^53 - 5876894224122036981984 * q^55 - 9121300938558448139840 * q^57 - 22913250483401428904208 * q^59 + 12462542938477863530088 * q^61 + 25160914682748748409760 * q^63 - 39966359416910506339344 * q^65 + 1327722087000187338000 * q^67 + 91326620713386312769664 * q^69 + 107087933176294058805024 * q^71 + 155463632157558765980280 * q^73 + 174501121789055311193072 * q^75 - 332298247608265373953920 * q^77 - 965133367885353973775040 * q^79 + 452218871763870073980076 * q^81 + 618081448580773491001680 * q^83 - 2251379405096414735385072 * q^85 + 376583198260927029773280 * q^87 + 34600911412223898467640 * q^89 - 4388806508692971365557824 * q^91 + 6041811404446910653519360 * q^93 + 9695233959199411285151712 * q^95 + 5248313571060446231270040 * q^97 + 2108801932420350407325296 * q^99

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(16))\) 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
16.26.a.a	$16$	$26$	16.a	1.a	$1$	$1$	$1$	$63.359$	\(\Q\)	None	✓				2.26.a.a	$1$	$0$	\(0\)	\(-97956\)	\(341005350\)	\(40882637368\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-97956q^{3}+341005350q^{5}+40882637368q^{7}+\cdots\)
16.26.a.b	$16$	$26$	16.a	1.a	$1$	$1$	$1$	$63.359$	\(\Q\)	None	✓				1.26.a.a	$1$	$0$	\(0\)	\(195804\)	\(-741989850\)	\(-39080597192\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+195804q^{3}-741989850q^{5}-39080597192q^{7}+\cdots\)
16.26.a.c	$16$	$26$	16.a	1.a	$1$	$2$	$2$	$63.359$	\(\Q(\sqrt{106705}) \)	None	✓				2.26.a.b	$1$	$0$	\(0\)	\(-379848\)	\(741953100\)	\(376536944\)		$-$	$-$	$2^{7}\cdot 3\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(-189924-\beta )q^{3}+(370976550+\cdots)q^{5}+\cdots\)
16.26.a.d	$16$	$26$	16.a	1.a	$1$	$2$	$2$	$63.359$	\(\Q(\sqrt{358121}) \)	None	✓				4.26.a.a	$1$	$0$	\(0\)	\(899640\)	\(-399350196\)	\(40518462320\)		$-$	$-$	$2^{7}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+(449820-\beta )q^{3}+(-199675098+\cdots)q^{5}+\cdots\)
16.26.a.e	$16$	$26$	16.a	1.a	$1$	$3$	$3$	$63.359$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓				8.26.a.b	$1$	$1$	\(0\)	\(-1255436\)	\(48510450\)	\(-5257017240\)		$+$	$+$	$2^{21}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(-418479+\beta _{1})q^{3}+(16170191+\cdots)q^{5}+\cdots\)
16.26.a.f	$16$	$26$	16.a	1.a	$1$	$3$	$3$	$63.359$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓				8.26.a.a	$1$	$1$	\(0\)	\(106356\)	\(163005426\)	\(12130107240\)		$+$	$+$	$2^{21}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)$	\(q+(35452+\beta _{1})q^{3}+(54335142-26\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_0(16)) \simeq \) \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)