Properties

Label 15.4.a
Level 15
Weight 4
Character orbit a
Rep. character \(\chi_{15}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 2
Sturm bound 8
Trace bound 2

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 15.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(15))\).

Total New Old
Modular forms 8 2 6
Cusp forms 4 2 2
Eisenstein series 4 0 4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(0\)

Trace form

\( 2q + 4q^{2} - 6q^{4} - 6q^{6} - 4q^{7} - 36q^{8} + 18q^{9} + O(q^{10}) \) \( 2q + 4q^{2} - 6q^{4} - 6q^{6} - 4q^{7} - 36q^{8} + 18q^{9} - 10q^{10} + 28q^{11} - 24q^{12} + 96q^{13} + 36q^{14} + 30q^{15} - 30q^{16} + 40q^{17} + 36q^{18} - 144q^{19} - 40q^{20} - 132q^{21} - 20q^{22} - 288q^{23} + 18q^{24} + 50q^{25} + 244q^{26} + 188q^{28} + 152q^{29} + 60q^{30} - 88q^{31} + 116q^{32} + 228q^{33} + 148q^{34} - 220q^{35} - 54q^{36} - 104q^{37} - 392q^{38} - 156q^{39} + 30q^{40} + 452q^{41} - 252q^{42} - 96q^{43} - 388q^{44} - 528q^{46} + 232q^{47} + 336q^{48} + 290q^{49} + 100q^{50} - 204q^{51} - 80q^{52} + 112q^{53} - 54q^{54} + 380q^{55} - 60q^{56} + 312q^{57} - 4q^{58} + 124q^{59} - 90q^{60} + 420q^{61} + 312q^{62} - 36q^{63} + 266q^{64} - 260q^{65} + 372q^{66} - 280q^{67} + 152q^{68} - 144q^{69} - 420q^{70} - 616q^{71} - 324q^{72} - 468q^{73} - 244q^{74} + 16q^{76} - 1728q^{77} - 600q^{78} - 760q^{79} + 560q^{80} + 162q^{81} + 1112q^{82} + 1368q^{83} + 444q^{84} - 340q^{85} + 88q^{86} + 924q^{87} - 276q^{88} + 1356q^{89} - 90q^{90} + 952q^{91} + 1056q^{92} - 1464q^{93} + 184q^{94} + 520q^{95} + 618q^{96} + 580q^{97} + 404q^{98} + 252q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(15))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5
15.4.a.a \(1\) \(0.885\) \(\Q\) None \(1\) \(3\) \(5\) \(-24\) \(-\) \(-\) \(q+q^{2}+3q^{3}-7q^{4}+5q^{5}+3q^{6}+\cdots\)
15.4.a.b \(1\) \(0.885\) \(\Q\) None \(3\) \(-3\) \(-5\) \(20\) \(+\) \(+\) \(q+3q^{2}-3q^{3}+q^{4}-5q^{5}-9q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(15))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(15)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - T + 8 T^{2} \))(\( 1 - 3 T + 8 T^{2} \))
$3$ (\( 1 - 3 T \))(\( 1 + 3 T \))
$5$ (\( 1 - 5 T \))(\( 1 + 5 T \))
$7$ (\( 1 + 24 T + 343 T^{2} \))(\( 1 - 20 T + 343 T^{2} \))
$11$ (\( 1 - 52 T + 1331 T^{2} \))(\( 1 + 24 T + 1331 T^{2} \))
$13$ (\( 1 - 22 T + 2197 T^{2} \))(\( 1 - 74 T + 2197 T^{2} \))
$17$ (\( 1 + 14 T + 4913 T^{2} \))(\( 1 - 54 T + 4913 T^{2} \))
$19$ (\( 1 + 20 T + 6859 T^{2} \))(\( 1 + 124 T + 6859 T^{2} \))
$23$ (\( 1 + 168 T + 12167 T^{2} \))(\( 1 + 120 T + 12167 T^{2} \))
$29$ (\( 1 - 230 T + 24389 T^{2} \))(\( 1 + 78 T + 24389 T^{2} \))
$31$ (\( 1 + 288 T + 29791 T^{2} \))(\( 1 - 200 T + 29791 T^{2} \))
$37$ (\( 1 + 34 T + 50653 T^{2} \))(\( 1 + 70 T + 50653 T^{2} \))
$41$ (\( 1 - 122 T + 68921 T^{2} \))(\( 1 - 330 T + 68921 T^{2} \))
$43$ (\( 1 + 188 T + 79507 T^{2} \))(\( 1 - 92 T + 79507 T^{2} \))
$47$ (\( 1 - 256 T + 103823 T^{2} \))(\( 1 + 24 T + 103823 T^{2} \))
$53$ (\( 1 + 338 T + 148877 T^{2} \))(\( 1 - 450 T + 148877 T^{2} \))
$59$ (\( 1 - 100 T + 205379 T^{2} \))(\( 1 - 24 T + 205379 T^{2} \))
$61$ (\( 1 - 742 T + 226981 T^{2} \))(\( 1 + 322 T + 226981 T^{2} \))
$67$ (\( 1 + 84 T + 300763 T^{2} \))(\( 1 + 196 T + 300763 T^{2} \))
$71$ (\( 1 + 328 T + 357911 T^{2} \))(\( 1 + 288 T + 357911 T^{2} \))
$73$ (\( 1 + 38 T + 389017 T^{2} \))(\( 1 + 430 T + 389017 T^{2} \))
$79$ (\( 1 + 240 T + 493039 T^{2} \))(\( 1 + 520 T + 493039 T^{2} \))
$83$ (\( 1 - 1212 T + 571787 T^{2} \))(\( 1 - 156 T + 571787 T^{2} \))
$89$ (\( 1 - 330 T + 704969 T^{2} \))(\( 1 - 1026 T + 704969 T^{2} \))
$97$ (\( 1 - 866 T + 912673 T^{2} \))(\( 1 + 286 T + 912673 T^{2} \))
show more
show less