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Properties

Label 6.28
Level 6
Weight 28
Dimension 5
Nonzero newspaces 1
Newform subspaces 4
Sturm bound 56
Trace bound 0

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Defining parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 28 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 4 \)
Sturm bound: \(56\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{28}(\Gamma_1(6))\).

Total New Old
Modular forms 29 5 24
Cusp forms 25 5 20
Eisenstein series 4 0 4

Trace form

\( 5 q - 8192 q^{2} - 1594323 q^{3} + 335544320 q^{4} + 6409250286 q^{5} + 13060694016 q^{6} - 596710016576 q^{7} - 549755813888 q^{8} + 12709329141645 q^{9} + O(q^{10}) \) \( 5 q - 8192 q^{2} - 1594323 q^{3} + 335544320 q^{4} + 6409250286 q^{5} + 13060694016 q^{6} - 596710016576 q^{7} - 549755813888 q^{8} + 12709329141645 q^{9} + 15078748274688 q^{10} - 242852704155924 q^{11} - 106993205379072 q^{12} - 160106320302722 q^{13} - 1609729302986752 q^{14} + 28469369834622 q^{15} + 22517998136852480 q^{16} - 54259888175988246 q^{17} - 20822964865671168 q^{18} - 337269444043159052 q^{19} + 430117505785135104 q^{20} + 234343132468933536 q^{21} + 2224352845485735936 q^{22} - 5271494118087511992 q^{23} + 876488338465357824 q^{24} + 12362615925471059171 q^{25} + 27762538500820779008 q^{26} - 4052555153018976267 q^{27} - 40044531349836529664 q^{28} + 2520673705582601862 q^{29} - 44209951814567706624 q^{30} + 322544335040452031032 q^{31} - 36893488147419103232 q^{32} + 416241711983386293804 q^{33} - 389500251680963837952 q^{34} + 176687013049309496064 q^{35} + 852908640897891041280 q^{36} + 3634555154410213611094 q^{37} + 947238983909879152640 q^{38} - 758384508465822961746 q^{39} + 1011917667256271634432 q^{40} - 18061484292399410153166 q^{41} + 13501897598277093556224 q^{42} + 9845921350191304362988 q^{43} - 16297569095232138510336 q^{44} + 16291454287191270152094 q^{45} - 14860086528940515852288 q^{46} - 132892977395463047362176 q^{47} - 7180192468708211294208 q^{48} + 160681686499720915263501 q^{49} - 182806962417749210488832 q^{50} + 259252527616714332926586 q^{51} - 10744553274735809527808 q^{52} - 609948910808651529830322 q^{53} + 33198531813531453579264 q^{54} + 366211146916649456369352 q^{55} - 108027104870952733769728 q^{56} + 871773942619663303812660 q^{57} + 679094763511524532961280 q^{58} - 626284228900551190903380 q^{59} + 1910547068397350289408 q^{60} - 563581048504437368738594 q^{61} - 1594477734790890481844224 q^{62} - 1516756800556165560381504 q^{63} + 1511157274518286468382720 q^{64} + 13123663524296596658415828 q^{65} - 1982246224567466441539584 q^{66} + 5688472790671149425964724 q^{67} - 3641319456257603266412544 q^{68} - 4104822443773877347662072 q^{69} - 22991735843672108755058688 q^{70} + 4566304861499685969191736 q^{71} - 1397405517247104682033152 q^{72} - 1778630202814347932777342 q^{73} + 26486932871469147131494400 q^{74} - 49809521763930332602553733 q^{75} - 22633769251647970951036928 q^{76} + 35044536704979596867553408 q^{77} - 20239205374311533318356992 q^{78} - 61484727001820599401872696 q^{79} + 28864697199753844915961856 q^{80} + 32305409446133366494661205 q^{81} + 86296976103723829391179776 q^{82} - 80290024337745786780209292 q^{83} + 15726501406191644892463104 q^{84} + 341528732721745319681017884 q^{85} - 234510727221370989789675520 q^{86} + 10684705128751020229829910 q^{87} + 149273792595715266868936704 q^{88} - 57029648008239629678061486 q^{89} + 38328154973404292744036352 q^{90} + 122919458621239228198632320 q^{91} - 353763981847534782369497088 q^{92} + 434767984651160654963191704 q^{93} + 672854635307389465879904256 q^{94} - 1982143008297205240664194440 q^{95} + 58820136703657666922151936 q^{96} + 1378334876978273384088183754 q^{97} + 674342002540433041353007104 q^{98} - 617298990011235339032370996 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{28}^{\mathrm{new}}(\Gamma_1(6))\)

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
6.28.a \(\chi_{6}(1, \cdot)\) 6.28.a.a 1 1
6.28.a.b 1
6.28.a.c 1
6.28.a.d 2

Decomposition of \(S_{28}^{\mathrm{old}}(\Gamma_1(6))\) into lower level spaces

\( S_{28}^{\mathrm{old}}(\Gamma_1(6)) \cong \) \(S_{28}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)