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Properties

Label 64.24
Level 64
Weight 24
Dimension 1645
Nonzero newspaces 4
Sturm bound 6144
Trace bound 1

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Defining parameters

Level: \( N \) = \( 64 = 2^{6} \)
Weight: \( k \) = \( 24 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(6144\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_1(64))\).

Total New Old
Modular forms 2980 1667 1313
Cusp forms 2908 1645 1263
Eisenstein series 72 22 50

Trace form

\( 1645 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 94143178837 q^{9} + O(q^{10}) \) \( 1645 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 94143178837 q^{9} - 8 q^{10} - 975574266682 q^{11} - 8 q^{12} + 14679969102048 q^{13} - 8 q^{14} + 69198046874996 q^{15} - 8 q^{16} + 225210108898490 q^{17} - 8 q^{18} - 33497748322222 q^{19} - 8 q^{20} - 2816418568096052 q^{21} + 4785813524104208 q^{22} - 8 q^{23} - 74351706934439968 q^{24} + 17441111860347641 q^{25} - 119676636113320048 q^{26} + 68199758786330304 q^{27} - 327561925545285888 q^{28} + 80364689641708328 q^{29} + 721561581296589672 q^{30} - 304901722756857968 q^{31} + 648515734309328672 q^{32} + 1043056332922357316 q^{33} - 2776252582182616368 q^{34} + 71740198139629916 q^{35} + 10378783640675711112 q^{36} - 4943314900604164912 q^{37} - 2865352596116028688 q^{38} - 8 q^{39} - 19127575392689278368 q^{40} + 4818265838526228470 q^{41} + 13542957315474336272 q^{42} + 9188667298883114718 q^{43} - 47789682858969276960 q^{44} - 35482899373563860124 q^{45} - 8 q^{46} + 49443184301680246056 q^{47} - 8 q^{48} - 35075009008795592967 q^{49} - 34966439551549591664 q^{50} + 381891615444244110388 q^{51} + 251623072484975867656 q^{52} - 229831036209146627600 q^{53} - 785917746657353619656 q^{54} - 910216462771797068232 q^{55} + 212114804072040827264 q^{56} + 99900145197504382816 q^{57} + 305751671071714354816 q^{58} - 2550246815375043144658 q^{59} - 809817707257018209512 q^{60} + 714638362101378972000 q^{61} + 273041109013632625640 q^{62} - 6314535828215606014084 q^{63} + 936666267548394583960 q^{64} + 2182227861493840290504 q^{65} - 4317809066449153402792 q^{66} - 8203926490142293918030 q^{67} + 5038320196177597905928 q^{68} - 3340648042030353132644 q^{69} - 18318806960414553463592 q^{70} - 6250758586149993887176 q^{71} + 21934396144216972744048 q^{72} - 599591944687612631050 q^{73} - 25736164443153075717520 q^{74} - 7641023408026869969438 q^{75} + 41101500300563992754360 q^{76} - 11752693703877066253684 q^{77} - 11054042081957264727440 q^{78} - 51828143942545736424488 q^{79} + 8368283073809527023776 q^{80} - 13867465829621891488427 q^{81} - 117457141548775293961048 q^{82} + 32909130597108510028794 q^{83} + 127126775583792257606696 q^{84} - 42245732889396088384432 q^{85} - 138305350969329855141072 q^{86} - 8 q^{87} + 170663450928121458162632 q^{88} - 24501159852268501459258 q^{89} - 463205160938228906250008 q^{90} - 85476927041001397522444 q^{91} + 548299211522405098470576 q^{92} + 230546749145371802417536 q^{93} - 182392326131070967546856 q^{94} - 418206809033540036489460 q^{95} - 335712426498832694406784 q^{96} + 474914106059241348653714 q^{97} + 1032286621648176347481200 q^{98} - 153989708813106085935310 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_1(64))\)

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
64.24.a \(\chi_{64}(1, \cdot)\) 64.24.a.a 1 1
64.24.a.b 1
64.24.a.c 1
64.24.a.d 2
64.24.a.e 2
64.24.a.f 2
64.24.a.g 2
64.24.a.h 3
64.24.a.i 3
64.24.a.j 3
64.24.a.k 3
64.24.a.l 4
64.24.a.m 6
64.24.a.n 6
64.24.a.o 6
64.24.b \(\chi_{64}(33, \cdot)\) 64.24.b.a 2 1
64.24.b.b 12
64.24.b.c 32
64.24.e \(\chi_{64}(17, \cdot)\) 64.24.e.a 90 2
64.24.g \(\chi_{64}(9, \cdot)\) None 0 4
64.24.i \(\chi_{64}(5, \cdot)\) n/a 1464 8

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

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_1(64)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)