↑

Properties

Label 10.16
Level 10
Weight 16
Dimension 13
Nonzero newspaces 2
Newform subspaces 5
Sturm bound 96
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 16 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 5 \)
Sturm bound: \(96\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(10))\).

Total New Old
Modular forms 49 13 36
Cusp forms 41 13 28
Eisenstein series 8 0 8

Trace form

\( 13 q + 128 q^{2} - 9632 q^{3} - 49152 q^{4} + 329525 q^{5} + 374272 q^{6} + 535804 q^{7} + 2097152 q^{8} - 32081191 q^{9} + O(q^{10}) \) \( 13 q + 128 q^{2} - 9632 q^{3} - 49152 q^{4} + 329525 q^{5} + 374272 q^{6} + 535804 q^{7} + 2097152 q^{8} - 32081191 q^{9} + 14403200 q^{10} + 74291676 q^{11} - 157810688 q^{12} + 744201478 q^{13} - 843293696 q^{14} - 400176200 q^{15} + 3489660928 q^{16} + 890757354 q^{17} + 654709376 q^{18} + 5718256060 q^{19} - 2838937600 q^{20} - 6873116744 q^{21} + 13494391296 q^{22} + 1886355348 q^{23} + 7876902912 q^{24} + 28275723125 q^{25} + 35608306432 q^{26} - 33283167920 q^{27} + 8778612736 q^{28} - 378760754610 q^{29} + 8378457600 q^{30} + 234286501176 q^{31} + 34359738368 q^{32} - 152670425424 q^{33} + 221272455424 q^{34} - 1624581833900 q^{35} + 899500621824 q^{36} + 1660154133694 q^{37} + 376608140800 q^{38} - 5979609034672 q^{39} + 91697971200 q^{40} + 6349243817226 q^{41} + 4441635721216 q^{42} - 2804034484232 q^{43} - 1910039445504 q^{44} - 4111920212175 q^{45} + 7669043950592 q^{46} + 10246116175284 q^{47} - 2585570312192 q^{48} - 22992059603379 q^{49} - 12704292400000 q^{50} + 49649536067936 q^{51} + 12192997015552 q^{52} - 25057737033762 q^{53} - 14762231546880 q^{54} - 33331218511700 q^{55} + 2546093522944 q^{56} + 19903369887200 q^{57} - 10077353329920 q^{58} - 57175150397820 q^{59} - 6735033139200 q^{60} + 85997166482726 q^{61} + 24327579406336 q^{62} + 9069525437468 q^{63} - 13194139533312 q^{64} + 100001032236550 q^{65} - 213315881363456 q^{66} - 98148968872856 q^{67} + 14594168487936 q^{68} + 256643990012968 q^{69} + 16689463987200 q^{70} - 134205399999024 q^{71} + 10726758416384 q^{72} + 66038638669618 q^{73} + 233113673553664 q^{74} + 167659423700000 q^{75} - 118623047843840 q^{76} - 516867155383872 q^{77} + 63914271450112 q^{78} + 1234426966039840 q^{79} + 88456193638400 q^{80} - 1568342837347347 q^{81} - 248954943124224 q^{82} - 169647139364832 q^{83} + 371057201381376 q^{84} + 907859952597850 q^{85} + 9545226445312 q^{86} - 764001995922720 q^{87} + 221092106993664 q^{88} - 560276244969630 q^{89} + 885924008169600 q^{90} - 926840819951464 q^{91} + 30906046021632 q^{92} - 660512111777584 q^{93} - 205082936252416 q^{94} - 1635773250666500 q^{95} + 100467874988032 q^{96} + 1420399684126474 q^{97} - 405707494390656 q^{98} + 3141687217590668 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.16.a \(\chi_{10}(1, \cdot)\) 10.16.a.a 1 1
10.16.a.b 1
10.16.a.c 1
10.16.a.d 2
10.16.b \(\chi_{10}(9, \cdot)\) 10.16.b.a 8 1

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)