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Properties

Label 7.23
Level 7
Weight 23
Dimension 41
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 92
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 23 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(92\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{23}(\Gamma_1(7))\).

Total New Old
Modular forms 47 47 0
Cusp forms 41 41 0
Eisenstein series 6 6 0

Trace form

\( 41 q - 3 q^{2} - 177150 q^{3} - 8388611 q^{4} - 65140350 q^{5} + 2627213953 q^{7} - 38066517063 q^{8} + 13281019473 q^{9} + O(q^{10}) \) \( 41 q - 3 q^{2} - 177150 q^{3} - 8388611 q^{4} - 65140350 q^{5} + 2627213953 q^{7} - 38066517063 q^{8} + 13281019473 q^{9} - 467948892300 q^{10} + 263802217464 q^{11} + 1339883191500 q^{12} + 8342499138561 q^{14} + 18907305848820 q^{15} - 90879261742951 q^{16} + 132200780053530 q^{17} - 432747484812927 q^{18} + 406539021312786 q^{19} + 458788905455538 q^{21} + 1083644725728858 q^{22} - 1336932987572472 q^{23} + 2132221481144712 q^{24} - 6642008664016015 q^{25} + 4631706025627464 q^{26} - 18477106351940635 q^{28} + 2930328014327754 q^{29} + 71754264743128560 q^{30} - 110579013704889990 q^{31} + 138131939907591945 q^{32} + 71043365674633770 q^{33} - 245070153819156750 q^{35} - 221693440465244055 q^{36} + 92447707971209672 q^{37} - 365603086302195120 q^{38} - 1048459252467970896 q^{39} + 4230965021667254400 q^{40} - 6840462120796440360 q^{42} + 3491229788883568058 q^{43} + 9344144704500959598 q^{44} - 10298297243286279180 q^{45} - 6882975481526294334 q^{46} + 10615044579928477050 q^{47} - 10907065581002433703 q^{49} - 3140089891373965455 q^{50} + 35979892061893216722 q^{51} - 54100783307796164520 q^{52} - 1404226908032776056 q^{53} + 110697258422197876032 q^{54} - 76507452422135491407 q^{56} + 15396580888840313460 q^{57} - 67283170066699040838 q^{58} + 29666790515816945490 q^{59} - 47593924252173619740 q^{60} - 109619603399071825950 q^{61} + 228649568551887197337 q^{63} + 147780233261822945041 q^{64} - 252980522361972281520 q^{65} + 516393503644744803132 q^{66} + 62671589702068553992 q^{67} - 817857457695710992980 q^{68} + 1057735834641642686880 q^{70} - 1264365380805727901598 q^{71} - 1102340973565545974847 q^{72} + 1556327797002677405370 q^{73} + 712149993637782451638 q^{74} - 2321130457862970052380 q^{75} + 3138458201453539634712 q^{77} + 865853352551218389120 q^{78} - 2406226342593947730104 q^{79} - 276606158314328336040 q^{80} + 193711596463373719743 q^{81} + 7494753756245697005400 q^{82} - 13566346663739803349892 q^{84} + 1761960133726721447460 q^{85} + 1301172719613402771738 q^{86} + 4588320993305192866980 q^{87} - 6733492520206861743822 q^{88} + 1965986019908957609274 q^{89} - 9114867987757598531808 q^{91} + 15279738520634971549530 q^{92} + 25258398982997860579170 q^{93} - 38414453223412415582448 q^{94} - 2572550015594693250390 q^{95} + 40644043435677141134640 q^{96} - 22677594488315380885467 q^{98} - 30792461694303066582582 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{23}^{\mathrm{new}}(\Gamma_1(7))\)

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

Label \(\chi\) Newforms Dimension \(\chi\) degree
7.23.b \(\chi_{7}(6, \cdot)\) 7.23.b.a 1 1
7.23.b.b 12
7.23.d \(\chi_{7}(3, \cdot)\) 7.23.d.a 28 2