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Properties

Label 7.26
Level 7
Weight 26
Dimension 45
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 104
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 26 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(104\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(7))\).

Total New Old
Modular forms 53 49 4
Cusp forms 47 45 2
Eisenstein series 6 4 2

Trace form

\( 45 q + 93 q^{2} - 139836 q^{3} - 4611 q^{4} + 883655214 q^{5} - 13079491206 q^{6} - 41377553679 q^{7} + 572385921855 q^{8} - 1380023122023 q^{9} + O(q^{10}) \) \( 45 q + 93 q^{2} - 139836 q^{3} - 4611 q^{4} + 883655214 q^{5} - 13079491206 q^{6} - 41377553679 q^{7} + 572385921855 q^{8} - 1380023122023 q^{9} - 8827842194658 q^{10} - 9267477242820 q^{11} + 71111128665738 q^{12} + 65676516052854 q^{13} + 844372027011513 q^{14} - 2118831007209288 q^{15} - 1484762475368271 q^{16} + 6651667423566378 q^{17} + 7882873094029299 q^{18} + 24893251061845188 q^{19} - 18495910040198304 q^{20} + 790115847364116 q^{21} - 218922829441297164 q^{22} + 279585626945396424 q^{23} + 280515610530266898 q^{24} - 874116389213906349 q^{25} + 3305788428317513460 q^{26} - 6453177153619695000 q^{27} + 11022032587870117317 q^{28} - 4937465304891094074 q^{29} + 5740773370860227334 q^{30} + 13740839828379457440 q^{31} + 12890788255192173183 q^{32} - 21696175546823174592 q^{33} + 70581886053972131358 q^{34} - 60613786846606484442 q^{35} + 269800290015355610409 q^{36} - 59818503161901688482 q^{37} - 105098853953137446840 q^{38} + 84226956485808936744 q^{39} - 68945588852281047360 q^{40} - 72156638602905645054 q^{41} + 331087917972327576102 q^{42} + 498376437550880558844 q^{43} - 1223282963365252546812 q^{44} - 1964788342749407355930 q^{45} + 3403947420478379403198 q^{46} + 2762045491560653882928 q^{47} - 11150105557979611206786 q^{48} + 3979554465588743061741 q^{49} + 5417609636050247227773 q^{50} - 12038553659747710232664 q^{51} - 15390345347896915903332 q^{52} + 12073346710596347465934 q^{53} + 20573217947025675272130 q^{54} - 54525717912305089444248 q^{55} + 7900094389147292531535 q^{56} + 80834382500719261166640 q^{57} - 67046237662513647773070 q^{58} - 92689442373681407756100 q^{59} + 262136645828429491643244 q^{60} - 54289282326449644283466 q^{61} - 120766129354909250468184 q^{62} - 46912781723724904651587 q^{63} + 503667884318295742517313 q^{64} - 223782113068819279017036 q^{65} - 286145926374634653175146 q^{66} + 421841842364126815969668 q^{67} + 508640844904860450403026 q^{68} - 1046265031572194474102592 q^{69} + 676039580834352247413306 q^{70} - 129319350936030258864120 q^{71} - 120268329683771312210625 q^{72} - 148892629569423495264366 q^{73} - 1214926953969222717091824 q^{74} - 111681918467402504828052 q^{75} + 789405324957038188315602 q^{76} - 186739422029885417778708 q^{77} - 1086594341666309531221152 q^{78} + 402473018093581421950560 q^{79} + 2612962555895081086482768 q^{80} - 863015007520434781174203 q^{81} - 4455956420524447292517714 q^{82} + 3900247778065086708215844 q^{83} - 7138994972174943299935758 q^{84} - 6552401407871927725744740 q^{85} + 13192679411324419439717736 q^{86} + 3439475314620483567226440 q^{87} - 15726031249905799691307840 q^{88} + 6892092896685058825816194 q^{89} + 32671992371566773027387036 q^{90} + 3009111050705478497553390 q^{91} - 29709600541758173975172312 q^{92} - 1921868108403782240000112 q^{93} + 13287724215081963897607794 q^{94} - 4958540361044327073914808 q^{95} + 4151033800130704031245218 q^{96} - 15299039447919860989916742 q^{97} + 13079625095830061170409133 q^{98} + 34449990339859651343704140 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(7))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
7.26.a \(\chi_{7}(1, \cdot)\) 7.26.a.a 6 1
7.26.a.b 7
7.26.c \(\chi_{7}(2, \cdot)\) 7.26.c.a 32 2

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_1(7))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_1(7)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)