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Properties

Label 64.20
Level 64
Weight 20
Dimension 1357
Nonzero newspaces 4
Sturm bound 5120
Trace bound 1

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Defining parameters

Level: \( N \) = \( 64 = 2^{6} \)
Weight: \( k \) = \( 20 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(5120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_1(64))\).

Total New Old
Modular forms 2468 1379 1089
Cusp forms 2396 1357 1039
Eisenstein series 72 22 50

Trace form

\( 1357 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 1162261477 q^{9} + O(q^{10}) \) \( 1357 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 1162261477 q^{9} - 8 q^{10} + 11401439590 q^{11} - 8 q^{12} + 51826863296 q^{13} - 8 q^{14} + 307546874996 q^{15} - 8 q^{16} - 56485706790 q^{17} - 8 q^{18} - 2711005682414 q^{19} - 8 q^{20} + 4585951224172 q^{21} - 25743871662064 q^{22} - 8 q^{23} + 125704945705952 q^{24} - 91003786384279 q^{25} + 237212306135952 q^{26} - 33727749530304 q^{27} - 300273370883328 q^{28} + 216906115317096 q^{29} + 261401642599272 q^{30} - 317275465928048 q^{31} + 156197009140512 q^{32} + 1483058429130404 q^{33} - 575171574278448 q^{34} - 1006937430747364 q^{35} + 2741392289816712 q^{36} + 3812119250206576 q^{37} - 3683234869037328 q^{38} - 8 q^{39} + 11727730771969632 q^{40} - 3748737897761802 q^{41} - 28251590849544688 q^{42} + 12774776518128574 q^{43} - 15459229388946976 q^{44} - 17476326650051004 q^{45} - 8 q^{46} + 22382609462055336 q^{47} - 8 q^{48} - 12659364337434215 q^{49} - 117434533274478704 q^{50} - 140608277533185932 q^{51} - 147474171051915512 q^{52} - 18631213032066800 q^{53} + 315760740658341688 q^{54} + 59809048657039928 q^{55} - 337754993107316352 q^{56} + 40901093104100416 q^{57} + 564710869907463808 q^{58} - 247444069367765234 q^{59} - 834905025478374632 q^{60} - 134845233947509696 q^{61} + 231484587706612712 q^{62} - 1608976996426874884 q^{63} + 646775840657479576 q^{64} + 379603852078849544 q^{65} - 2149677962138617768 q^{66} - 415551272718166670 q^{67} + 1422764051197365256 q^{68} + 1019780546402447356 q^{69} - 1448578674510936872 q^{70} + 3332717714276511288 q^{71} - 1616527279514677904 q^{72} - 30546095277116426 q^{73} + 3962913278640095856 q^{74} + 2677845341699494722 q^{75} - 7809159342924433224 q^{76} - 1250723257104163924 q^{77} + 611833215828260464 q^{78} + 12388012457735721304 q^{79} - 12991356620956012384 q^{80} + 1448506550755610005 q^{81} + 16941486229463184552 q^{82} - 4143782594170027526 q^{83} - 27508330183408710616 q^{84} + 6800214252185519088 q^{85} + 29987745129531418416 q^{86} - 8 q^{87} - 15167508609102318648 q^{88} - 25902494912674473722 q^{89} - 20069076344906250008 q^{90} + 14985703834973392628 q^{91} + 71757296995077161136 q^{92} - 15077460690298057664 q^{93} - 30668204964906791912 q^{94} + 2312387541647240460 q^{95} - 53311128660256776832 q^{96} - 10968707747675161102 q^{97} + 111104584140484022384 q^{98} + 42135969399592208498 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_1(64))\)

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
64.20.a \(\chi_{64}(1, \cdot)\) 64.20.a.a 1 1
64.20.a.b 1
64.20.a.c 1
64.20.a.d 1
64.20.a.e 1
64.20.a.f 1
64.20.a.g 1
64.20.a.h 1
64.20.a.i 1
64.20.a.j 2
64.20.a.k 2
64.20.a.l 3
64.20.a.m 3
64.20.a.n 4
64.20.a.o 4
64.20.a.p 5
64.20.a.q 5
64.20.b \(\chi_{64}(33, \cdot)\) 64.20.b.a 2 1
64.20.b.b 12
64.20.b.c 24
64.20.e \(\chi_{64}(17, \cdot)\) 64.20.e.a 74 2
64.20.g \(\chi_{64}(9, \cdot)\) None 0 4
64.20.i \(\chi_{64}(5, \cdot)\) n/a 1208 8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_1(64)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)