Properties

Label 15.10
Level 15
Weight 10
Dimension 46
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 160
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(160\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(15))\).

Total New Old
Modular forms 80 54 26
Cusp forms 64 46 18
Eisenstein series 16 8 8

Trace form

\( 46 q + 68 q^{2} - 150 q^{3} + 344 q^{4} - 690 q^{5} - 7140 q^{6} - 21188 q^{7} + 67932 q^{8} - 13122 q^{9} + O(q^{10}) \) \( 46 q + 68 q^{2} - 150 q^{3} + 344 q^{4} - 690 q^{5} - 7140 q^{6} - 21188 q^{7} + 67932 q^{8} - 13122 q^{9} + 18520 q^{10} - 159064 q^{11} + 233412 q^{12} + 170148 q^{13} + 531816 q^{14} - 61290 q^{15} - 1915024 q^{16} - 420520 q^{17} + 1440948 q^{18} + 1510496 q^{19} + 1173100 q^{20} - 3242652 q^{21} - 6848280 q^{22} + 3122496 q^{23} + 4436208 q^{24} + 9847270 q^{25} - 6770392 q^{26} + 4786830 q^{27} - 9172776 q^{28} - 7070108 q^{29} - 15876960 q^{30} + 12093928 q^{31} + 17859412 q^{32} + 18442884 q^{33} - 2414552 q^{34} - 21174680 q^{35} - 31019304 q^{36} - 10493548 q^{37} - 2385976 q^{38} + 7411824 q^{39} + 124068200 q^{40} + 117594724 q^{41} + 2551536 q^{42} - 122810748 q^{43} - 177425288 q^{44} - 125161290 q^{45} - 96583992 q^{46} + 51128264 q^{47} + 340587828 q^{48} + 135923910 q^{49} + 94360700 q^{50} - 109600476 q^{51} - 209781040 q^{52} - 114062224 q^{53} - 23383404 q^{54} + 128495720 q^{55} - 136664640 q^{56} + 45495684 q^{57} - 415626152 q^{58} + 417468464 q^{59} - 208559160 q^{60} + 185675724 q^{61} - 31830936 q^{62} + 14879472 q^{63} + 452073416 q^{64} - 172199200 q^{65} + 324822624 q^{66} - 331042820 q^{67} + 717440536 q^{68} + 172304496 q^{69} + 1164742440 q^{70} - 73747472 q^{71} - 1088344908 q^{72} + 37028316 q^{73} - 2296939904 q^{74} - 390483390 q^{75} - 2207705040 q^{76} + 72064224 q^{77} - 137852280 q^{78} + 589394400 q^{79} + 733243180 q^{80} + 2853197046 q^{81} + 5664251624 q^{82} + 804884184 q^{83} - 1030301856 q^{84} - 2307340580 q^{85} + 245612816 q^{86} - 2840994132 q^{87} - 2764190328 q^{88} + 27621876 q^{89} + 196282680 q^{90} - 5025897832 q^{91} - 2807106528 q^{92} - 1123759992 q^{93} + 2549830744 q^{94} + 2062249640 q^{95} + 9194942832 q^{96} + 5375198660 q^{97} + 5935831732 q^{98} - 98992368 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(15))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
15.10.a \(\chi_{15}(1, \cdot)\) 15.10.a.a 1 1
15.10.a.b 1
15.10.a.c 2
15.10.a.d 2
15.10.b \(\chi_{15}(4, \cdot)\) 15.10.b.a 8 1
15.10.e \(\chi_{15}(2, \cdot)\) 15.10.e.a 32 2

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(15)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)