↑

Properties

Label 64.18
Level 64
Weight 18
Dimension 1213
Nonzero newspaces 4
Sturm bound 4608
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 64 = 2^{6} \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(4608\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(64))\).

Total New Old
Modular forms 2212 1235 977
Cusp forms 2140 1213 927
Eisenstein series 72 22 50

Trace form

\( 1213 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 129140173 q^{9} + O(q^{10}) \) \( 1213 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 129140173 q^{9} - 8 q^{10} - 8886922 q^{11} - 8 q^{12} - 442574736 q^{13} - 8 q^{14} - 20503125004 q^{15} - 8 q^{16} + 29956502378 q^{17} - 8 q^{18} + 37768314098 q^{19} - 8 q^{20} - 362812146308 q^{21} - 1539487376880 q^{22} - 8 q^{23} + 3596116585952 q^{24} - 933917499839 q^{25} - 7245720377968 q^{26} + 3332122990080 q^{27} + 2722742834432 q^{28} - 8141002766584 q^{29} + 882936756072 q^{30} + 10234692449296 q^{31} + 2922177926432 q^{32} - 45066401458540 q^{33} - 21098156588848 q^{34} + 24684351187196 q^{35} + 129299521934472 q^{36} - 13277430784640 q^{37} - 141039948893968 q^{38} - 8 q^{39} + 234333680193632 q^{40} - 120864339283978 q^{41} - 36519870838768 q^{42} - 22474846890898 q^{43} - 151191543368736 q^{44} + 340373274483828 q^{45} - 8 q^{46} - 476225733235224 q^{47} - 8 q^{48} + 641906541176169 q^{49} - 1336539363374192 q^{50} - 1168459367891180 q^{51} + 2273909036838664 q^{52} - 970722523313312 q^{53} - 1211057852430536 q^{54} - 6150557222727624 q^{55} + 2497695544472960 q^{56} - 768369709267856 q^{57} - 8071669246002560 q^{58} - 306404558725954 q^{59} + 16194667217066776 q^{60} - 3454795454866320 q^{61} - 4947553071225880 q^{62} + 23885055970803260 q^{63} - 13160501167036520 q^{64} - 5555546063074584 q^{65} + 35164415067670616 q^{66} - 21741059700304558 q^{67} - 11519792360049656 q^{68} + 231950983562860 q^{69} - 30099041179396904 q^{70} - 24737621153058760 q^{71} + 61147595469597040 q^{72} - 19277013948846090 q^{73} - 46832069295298960 q^{74} + 119887433022751410 q^{75} + 17795309333371064 q^{76} + 11746433416721276 q^{77} - 116970337322778512 q^{78} + 133792443290946072 q^{79} + 30090655383590048 q^{80} - 44426988625049867 q^{81} + 117969223605039272 q^{82} + 93896005089331194 q^{83} - 18713817771474904 q^{84} - 153632656361690752 q^{85} - 244926728152677072 q^{86} - 8 q^{87} + 302843563536560072 q^{88} + 262688965631579942 q^{89} - 114380820506250008 q^{90} - 156528290251705356 q^{91} - 703425767746084176 q^{92} - 110702447243918048 q^{93} + 374658285512135704 q^{94} + 432608377121015820 q^{95} + 635030073138832256 q^{96} - 307572667667045726 q^{97} - 994394690199939472 q^{98} - 323325870756406510 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(64))\)

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
64.18.a \(\chi_{64}(1, \cdot)\) 64.18.a.a 1 1
64.18.a.b 1
64.18.a.c 1
64.18.a.d 1
64.18.a.e 1
64.18.a.f 2
64.18.a.g 2
64.18.a.h 2
64.18.a.i 2
64.18.a.j 2
64.18.a.k 2
64.18.a.l 2
64.18.a.m 2
64.18.a.n 4
64.18.a.o 4
64.18.a.p 4
64.18.b \(\chi_{64}(33, \cdot)\) 64.18.b.a 2 1
64.18.b.b 8
64.18.b.c 24
64.18.e \(\chi_{64}(17, \cdot)\) 64.18.e.a 66 2
64.18.g \(\chi_{64}(9, \cdot)\) None 0 4
64.18.i \(\chi_{64}(5, \cdot)\) n/a 1080 8

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

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(64)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 1}\)