Properties

Label 8015.2.a
Level 8015
Weight 2
Character orbit a
Rep. character \(\chi_{8015}(1,\cdot)\)
Character field \(\Q\)
Dimension 455
Newform subspaces 15
Sturm bound 1840
Trace bound 3

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Defining parameters

Level: \( N \) \(=\) \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8015.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(1840\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8015))\).

Total New Old
Modular forms 924 455 469
Cusp forms 917 455 462
Eisenstein series 7 0 7

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

\(5\)\(7\)\(229\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(52\)
\(+\)\(+\)\(-\)\(-\)\(63\)
\(+\)\(-\)\(+\)\(-\)\(68\)
\(+\)\(-\)\(-\)\(+\)\(45\)
\(-\)\(+\)\(+\)\(-\)\(67\)
\(-\)\(+\)\(-\)\(+\)\(44\)
\(-\)\(-\)\(+\)\(+\)\(41\)
\(-\)\(-\)\(-\)\(-\)\(75\)
Plus space\(+\)\(182\)
Minus space\(-\)\(273\)

Trace form

\( 455q + 5q^{2} + 4q^{3} + 453q^{4} - q^{5} + 20q^{6} + 3q^{7} + 33q^{8} + 471q^{9} + O(q^{10}) \) \( 455q + 5q^{2} + 4q^{3} + 453q^{4} - q^{5} + 20q^{6} + 3q^{7} + 33q^{8} + 471q^{9} - 3q^{10} + 8q^{11} + 20q^{12} - 14q^{13} + q^{14} + 453q^{16} + 14q^{17} + 25q^{18} + 12q^{19} - 7q^{20} + 20q^{22} + 32q^{23} + 12q^{24} + 455q^{25} - 2q^{26} + 64q^{27} + 21q^{28} + 22q^{29} - 4q^{30} + 16q^{31} + 81q^{32} + 72q^{33} + 26q^{34} + 7q^{35} + 481q^{36} + 2q^{37} + 4q^{38} + 68q^{39} - 15q^{40} + 38q^{41} - 12q^{42} + 12q^{43} + 20q^{44} + 3q^{45} - 32q^{46} + 8q^{47} + 4q^{48} + 455q^{49} + 5q^{50} - 4q^{51} + 14q^{52} - 30q^{53} - 16q^{54} + 4q^{55} - 3q^{56} + 24q^{57} + 22q^{58} + 28q^{59} - 12q^{60} - 30q^{61} + 16q^{62} + 7q^{63} + 509q^{64} + 14q^{65} + 24q^{66} + 28q^{67} + 114q^{68} - 8q^{69} - 3q^{70} + 16q^{71} + 149q^{72} + 38q^{73} + 46q^{74} + 4q^{75} + 76q^{76} + 20q^{77} + 72q^{78} + 12q^{79} + q^{80} + 559q^{81} + 98q^{82} - 12q^{83} - 12q^{84} - 6q^{85} + 68q^{86} - 40q^{87} + 108q^{88} - 2q^{89} - 7q^{90} - 2q^{91} + 32q^{92} + 16q^{93} + 8q^{94} - 4q^{95} + 108q^{96} + 78q^{97} + 5q^{98} - 20q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8015))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 7 229
8015.2.a.a \(1\) \(64.000\) \(\Q\) None \(-2\) \(-3\) \(1\) \(1\) \(-\) \(-\) \(-\) \(q-2q^{2}-3q^{3}+2q^{4}+q^{5}+6q^{6}+\cdots\)
8015.2.a.b \(1\) \(64.000\) \(\Q\) None \(-1\) \(-2\) \(1\) \(1\) \(-\) \(-\) \(+\) \(q-q^{2}-2q^{3}-q^{4}+q^{5}+2q^{6}+q^{7}+\cdots\)
8015.2.a.c \(1\) \(64.000\) \(\Q\) None \(-1\) \(1\) \(1\) \(1\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
8015.2.a.d \(1\) \(64.000\) \(\Q\) None \(1\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{4}+q^{5}+q^{7}-3q^{8}-3q^{9}+\cdots\)
8015.2.a.e \(1\) \(64.000\) \(\Q\) None \(1\) \(2\) \(-1\) \(-1\) \(+\) \(+\) \(-\) \(q+q^{2}+2q^{3}-q^{4}-q^{5}+2q^{6}-q^{7}+\cdots\)
8015.2.a.f \(1\) \(64.000\) \(\Q\) None \(2\) \(1\) \(1\) \(1\) \(-\) \(-\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+q^{7}+\cdots\)
8015.2.a.g \(3\) \(64.000\) 3.3.148.1 None \(1\) \(-1\) \(-3\) \(-3\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
8015.2.a.h \(38\) \(64.000\) None \(-6\) \(-9\) \(38\) \(38\) \(-\) \(-\) \(+\)
8015.2.a.i \(44\) \(64.000\) None \(-2\) \(0\) \(44\) \(-44\) \(-\) \(+\) \(-\)
8015.2.a.j \(45\) \(64.000\) None \(-6\) \(0\) \(-45\) \(45\) \(+\) \(-\) \(-\)
8015.2.a.k \(49\) \(64.000\) None \(-3\) \(-10\) \(-49\) \(-49\) \(+\) \(+\) \(+\)
8015.2.a.l \(62\) \(64.000\) None \(2\) \(11\) \(-62\) \(-62\) \(+\) \(+\) \(-\)
8015.2.a.m \(67\) \(64.000\) None \(3\) \(0\) \(67\) \(-67\) \(-\) \(+\) \(+\)
8015.2.a.n \(68\) \(64.000\) None \(9\) \(0\) \(-68\) \(68\) \(+\) \(-\) \(+\)
8015.2.a.o \(73\) \(64.000\) None \(7\) \(14\) \(73\) \(73\) \(-\) \(-\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8015))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8015)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(229))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1145))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1603))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( 1 - 2 T + 2 T^{2} \))(\( 1 - T + 3 T^{2} - 3 T^{3} + 6 T^{4} - 4 T^{5} + 8 T^{6} \))
$3$ (\( 1 + 3 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 + T - 7 T^{3} + 9 T^{5} + 27 T^{6} \))
$5$ (\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( ( 1 + T )^{3} \))
$7$ (\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( ( 1 + T )^{3} \))
$11$ (\( 1 - 5 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 4 T + 29 T^{2} + 68 T^{3} + 319 T^{4} + 484 T^{5} + 1331 T^{6} \))
$13$ (\( 1 + T + 13 T^{2} \))(\( 1 + 7 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - 3 T + 13 T^{2} \))(\( 1 + 3 T + 8 T^{2} - 17 T^{3} + 104 T^{4} + 507 T^{5} + 2197 T^{6} \))
$17$ (\( 1 - 3 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + T + 17 T^{2} \))(\( 1 + 4 T + 43 T^{2} + 120 T^{3} + 731 T^{4} + 1156 T^{5} + 4913 T^{6} \))
$19$ (\( 1 - 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( ( 1 + 19 T^{2} )^{3} \))
$23$ (\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 + 4 T + 29 T^{2} + 116 T^{3} + 667 T^{4} + 2116 T^{5} + 12167 T^{6} \))
$29$ (\( 1 - 5 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 - 10 T + 111 T^{2} - 576 T^{3} + 3219 T^{4} - 8410 T^{5} + 24389 T^{6} \))
$31$ (\( 1 - 2 T + 31 T^{2} \))(\( 1 + 9 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 9 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 6 T + 21 T^{2} + 56 T^{3} + 651 T^{4} - 5766 T^{5} + 29791 T^{6} \))
$37$ (\( 1 + 8 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 6 T + 75 T^{2} + 336 T^{3} + 2775 T^{4} + 8214 T^{5} + 50653 T^{6} \))
$41$ (\( 1 - 6 T + 41 T^{2} \))(\( 1 + 5 T + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 26 T + 339 T^{2} + 2712 T^{3} + 13899 T^{4} + 43706 T^{5} + 68921 T^{6} \))
$43$ (\( 1 + 4 T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 3 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 16 T + 193 T^{2} - 1408 T^{3} + 8299 T^{4} - 29584 T^{5} + 79507 T^{6} \))
$47$ (\( 1 + T + 47 T^{2} \))(\( 1 - 5 T + 47 T^{2} \))(\( 1 + 10 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 + 8 T + 157 T^{2} + 756 T^{3} + 7379 T^{4} + 17672 T^{5} + 103823 T^{6} \))
$53$ (\( 1 - 6 T + 53 T^{2} \))(\( 1 + 5 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 5 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 2 T + 155 T^{2} - 208 T^{3} + 8215 T^{4} - 5618 T^{5} + 148877 T^{6} \))
$59$ (\( 1 + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 15 T + 182 T^{2} + 1459 T^{3} + 10738 T^{4} + 52215 T^{5} + 205379 T^{6} \))
$61$ (\( 1 - 10 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - T + 86 T^{2} - 285 T^{3} + 5246 T^{4} - 3721 T^{5} + 226981 T^{6} \))
$67$ (\( 1 - 8 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 + 6 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 12 T + 201 T^{2} + 1460 T^{3} + 13467 T^{4} + 53868 T^{5} + 300763 T^{6} \))
$71$ (\( 1 - 12 T + 71 T^{2} \))(\( 1 + 3 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 9 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 18 T + 281 T^{2} - 2456 T^{3} + 19951 T^{4} - 90738 T^{5} + 357911 T^{6} \))
$73$ (\( 1 + 10 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 11 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 15 T + 224 T^{2} + 1879 T^{3} + 16352 T^{4} + 79935 T^{5} + 389017 T^{6} \))
$79$ (\( 1 - 9 T + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( 1 - 3 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 - 9 T + 79 T^{2} \))(\( 1 - 5 T + 180 T^{2} - 551 T^{3} + 14220 T^{4} - 31205 T^{5} + 493039 T^{6} \))
$83$ (\( 1 - 4 T + 83 T^{2} \))(\( 1 + 2 T + 83 T^{2} \))(\( 1 - 7 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 7 T + 260 T^{2} + 1163 T^{3} + 21580 T^{4} + 48223 T^{5} + 571787 T^{6} \))
$89$ (\( 1 - 12 T + 89 T^{2} \))(\( 1 + 5 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 9 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 + 6 T - T^{2} - 172 T^{3} - 89 T^{4} + 47526 T^{5} + 704969 T^{6} \))
$97$ (\( 1 - 11 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 24 T + 419 T^{2} + 4528 T^{3} + 40643 T^{4} + 225816 T^{5} + 912673 T^{6} \))
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