Properties

Label 1.26
Level 1
Weight 26
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 2
Trace bound 0

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 26 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(1))\).

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

Trace form

\( q - 48 q^{2} - 195804 q^{3} - 33552128 q^{4} - 741989850 q^{5} + 9398592 q^{6} + 39080597192 q^{7} + 3221114880 q^{8} - 808949403027 q^{9} + O(q^{10}) \) \( 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} + O(q^{100}) \)

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(1))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1.26.a \(\chi_{1}(1, \cdot)\) 1.26.a.a 1 1