Space of modular forms of level 1, weight 26, and trivial character

• Label: 1.26.a
• Level: $1$
• Weight: $26$
• Character orbit: 1.a
• Rep. character: $\chi_{1}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $2$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(2\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(1))\).

	Total	New	Old
Modular forms	2	2	0
Cusp forms	1	1	0
Eisenstein series	1	1	0

Trace form

q - 48 * q^2 - 195804 * q^3 - 33552128 * q^4 - 741989850 * q^5 + 9398592 * q^6 + 39080597192 * q^7 + 3221114880 * q^8 - 808949403027 * q^9 + 35615512800 * q^10 + 8419515299052 * q^11 + 6569640870912 * q^12 - 81651045335314 * q^13 - 1875868665216 * q^14 + 145284580589400 * q^15 + 1125667983917056 * q^16 - 2519900028948078 * q^17 + 38829571345296 * q^18 - 6082056370308940 * q^19 + 24895338421900800 * q^20 - 7652137252582368 * q^21 - 404136734354496 * q^22 - 94995280296320424 * q^23 - 630707177963520 * q^24 + 252525713626069375 * q^25 + 3919250176095072 * q^26 + 324298027793675880 * q^27 - 1311237199302424576 * q^28 - 271246959476737410 * q^29 - 6973659868291200 * q^30 + 4291666067521509152 * q^31 - 162114743433166848 * q^32 - 1648574773615577808 * q^33 + 120955201389507744 * q^34 - 28997406448402501200 * q^35 + 27141973915885491456 * q^36 + 20301484446109126982 * q^37 + 291938705774829120 * q^38 + 15987601280835822456 * q^39 - 2390034546643968000 * q^40 - 183744249574071224598 * q^41 + 367302588123953664 * q^42 + 300901824185586335756 * q^43 - 282492655011750982656 * q^44 + 600232246209593275950 * q^45 + 4559773454223380352 * q^46 - 924361048064704868688 * q^47 - 220410293922895233024 * q^48 + 186224457219393384057 * q^49 - 12121234254051330000 * q^50 + 493406505268149464712 * q^51 + 2739566324424258248192 * q^52 - 990292205554990470954 * q^53 - 15566305334096442240 * q^54 - 6247194893816298622200 * q^55 + 125883093134437416960 * q^56 + 1190890965531971687760 * q^57 + 13019854054883395680 * q^58 + 13052569416454201837980 * q^59 - 4874606844361864243200 * q^60 + 9015451224701414617502 * q^61 - 205999971241032439296 * q^62 - 31614225768407052500184 * q^63 - 37763368313237157183488 * q^64 + 60584246880692834562900 * q^65 + 79131589133547734784 * q^66 - 26689067808908579702428 * q^67 + 84548008318469618409984 * q^68 + 18600455863140724300896 * q^69 + 1391875509523320057600 * q^70 - 192390516186217637440248 * q^71 - 2605718959257386741760 * q^72 + 42404584838092453858826 * q^73 - 974471253413238095136 * q^74 - 49445544830838887902500 * q^75 + 204065933839820954424320 * q^76 + 329039685954132631461984 * q^77 - 767404861480119477888 * q^78 - 271681055025772277197360 * q^79 - 835234218536418793881600 * q^80 + 621914763766378892976441 * q^81 + 8819723979555418780704 * q^82 - 931454457307013524361484 * q^83 + 256745488572211941679104 * q^84 + 1869740244494180053008300 * q^85 - 14443287560908144116288 * q^86 + 53111239653383091827640 * q^87 + 27120226012164047093760 * q^88 - 1763635518049807316502630 * q^89 - 28811147818060477245600 * q^90 - 3190971613055137006838288 * q^91 + 3187293803898020795062272 * q^92 - 840325382684981577998208 * q^93 + 44369330307105833697024 * q^94 + 4512824093897074844259000 * q^95 + 31742715223187801505792 * q^96 + 2829240869926872086187362 * q^97 - 8938773946530882434736 * q^98 - 6810961874944808779030404 * q^99

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\) 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				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.26.a.a	$1$	$26$	1.a	1.a	$1$	$1$	$1$	$3.960$	\(\Q\)	None	✓	✓	✓	✓	1.26.a.a	$1$	$1$	\(-48\)	\(-195804\)	\(-741989850\)	\(39080597192\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-48q^{2}-195804q^{3}-33552128q^{4}+\cdots\)