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Properties

Label 22.14
Level 22
Weight 14
Dimension 61
Nonzero newspaces 2
Newform subspaces 6
Sturm bound 420
Trace bound 1

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Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 6 \)
Sturm bound: \(420\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(22))\).

Total New Old
Modular forms 205 61 144
Cusp forms 185 61 124
Eisenstein series 20 0 20

Trace form

\( 61 q + 1200 q^{3} - 16384 q^{4} + 106920 q^{5} + 6464 q^{6} + 763610 q^{7} - 9560032 q^{9} + O(q^{10}) \) \( 61 q + 1200 q^{3} - 16384 q^{4} + 106920 q^{5} + 6464 q^{6} + 763610 q^{7} - 9560032 q^{9} + 17864320 q^{10} - 11005534 q^{11} - 19619840 q^{12} + 46107890 q^{13} - 19222912 q^{14} - 37995610 q^{15} - 67108864 q^{16} + 373590700 q^{17} - 252287680 q^{18} - 505092125 q^{19} + 437944320 q^{20} - 35021388 q^{21} - 54067200 q^{22} - 2051471700 q^{23} + 26476544 q^{24} - 4000531860 q^{25} - 4847416576 q^{26} + 16602419505 q^{27} + 4693237760 q^{28} - 25776793600 q^{29} - 8052167040 q^{30} - 5703044858 q^{31} + 5368709120 q^{32} + 32630359795 q^{33} - 20818216192 q^{34} - 106759684580 q^{35} - 17358794752 q^{36} + 85314150780 q^{37} + 49437425280 q^{38} - 78487415614 q^{39} - 13586923520 q^{40} - 69241191208 q^{41} + 30790778240 q^{42} + 275383139730 q^{43} - 50243293184 q^{44} - 420879674590 q^{45} - 5284293376 q^{46} + 397555025720 q^{47} + 20132659200 q^{48} + 162267958512 q^{49} - 691829338880 q^{50} - 333774902003 q^{51} - 70745210880 q^{52} + 1397100972410 q^{53} + 1211741821440 q^{54} + 557060328070 q^{55} - 260919263232 q^{56} - 1962597870975 q^{57} - 714418050560 q^{58} + 624766255205 q^{59} + 1088951500800 q^{60} - 835558753618 q^{61} + 109223928960 q^{62} + 4690081118680 q^{63} - 274877906944 q^{64} - 1818215510060 q^{65} - 3760921554176 q^{66} + 3152692850650 q^{67} + 1530227507200 q^{68} - 1365012752274 q^{69} - 2193344480000 q^{70} - 2206118535408 q^{71} - 1897340600320 q^{72} + 3517436683660 q^{73} + 2307708222208 q^{74} - 258676904345 q^{75} + 2801861304320 q^{76} - 5586287509800 q^{77} + 2151752220160 q^{78} + 4739244317010 q^{79} - 836679761920 q^{80} - 29726975479209 q^{81} - 7513501629760 q^{82} + 16155763467485 q^{83} + 3234169126912 q^{84} + 5636802716270 q^{85} - 10679601747136 q^{86} + 3386852073700 q^{87} - 5778778357760 q^{88} + 3452663443520 q^{89} + 17714495606400 q^{90} - 1386012676308 q^{91} + 4238672977920 q^{92} - 19087970312830 q^{93} - 48431461036032 q^{94} - 12358886229490 q^{95} - 6597069766656 q^{96} + 17225663341515 q^{97} + 63381313385280 q^{98} + 103249481578978 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(22))\)

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
22.14.a \(\chi_{22}(1, \cdot)\) 22.14.a.a 2 1
22.14.a.b 2
22.14.a.c 2
22.14.a.d 3
22.14.c \(\chi_{22}(3, \cdot)\) 22.14.c.a 24 4
22.14.c.b 28

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(22))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(22)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)