Properties

Label 8033.2.a
Level $8033$
Weight $2$
Character orbit 8033.a
Rep. character $\chi_{8033}(1,\cdot)$
Character field $\Q$
Dimension $645$
Newform subspaces $5$
Sturm bound $1390$
Trace bound $1$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 8033 = 29 \cdot 277 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8033.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(1390\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8033))\).

Total New Old
Modular forms 696 645 51
Cusp forms 693 645 48
Eisenstein series 3 0 3

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

\(29\)\(277\)FrickeDim.
\(+\)\(+\)\(+\)\(153\)
\(+\)\(-\)\(-\)\(169\)
\(-\)\(+\)\(-\)\(169\)
\(-\)\(-\)\(+\)\(154\)
Plus space\(+\)\(307\)
Minus space\(-\)\(338\)

Trace form

\( 645q + q^{2} - 4q^{3} + 643q^{4} + 2q^{5} + 8q^{7} - 3q^{8} + 641q^{9} + O(q^{10}) \) \( 645q + q^{2} - 4q^{3} + 643q^{4} + 2q^{5} + 8q^{7} - 3q^{8} + 641q^{9} - 2q^{10} - 4q^{11} + 10q^{13} + 4q^{14} - 20q^{15} + 651q^{16} - 6q^{17} - 3q^{18} - 8q^{19} + 14q^{20} + 16q^{21} + 24q^{22} - 8q^{24} + 663q^{25} - 18q^{26} - 28q^{27} + 44q^{28} + q^{29} - 40q^{30} - 12q^{31} - 35q^{32} - 12q^{33} - 18q^{34} + 547q^{36} + 22q^{37} - 24q^{38} + 40q^{39} - 22q^{40} - 2q^{41} - 64q^{42} + 20q^{43} - 16q^{44} + 22q^{45} - 24q^{46} - 28q^{47} + 16q^{48} + 685q^{49} - 5q^{50} - 16q^{51} + 22q^{52} - 18q^{53} + 16q^{54} + 28q^{55} + 32q^{56} - 8q^{57} + q^{58} - 40q^{60} - 10q^{61} + 60q^{63} + 679q^{64} - 40q^{65} - 28q^{66} - 4q^{67} - 38q^{68} - 88q^{69} - 24q^{70} + 8q^{71} - 83q^{72} + 22q^{73} + 30q^{74} + 4q^{75} - 28q^{76} - 24q^{77} + 28q^{78} + 24q^{79} + 14q^{80} + 573q^{81} - 86q^{82} + 28q^{83} + 128q^{84} + 48q^{85} - 72q^{86} + 4q^{87} + 32q^{88} + 22q^{89} + 42q^{90} + 96q^{91} - 48q^{92} - 24q^{93} + 36q^{94} + 4q^{95} - 136q^{96} - 6q^{97} - 7q^{98} - 80q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8033))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 29 277
8033.2.a.a \(1\) \(64.144\) \(\Q\) None \(1\) \(1\) \(-3\) \(2\) \(-\) \(+\) \(q+q^{2}+q^{3}-q^{4}-3q^{5}+q^{6}+2q^{7}+\cdots\)
8033.2.a.b \(153\) \(64.144\) None \(-3\) \(-12\) \(-11\) \(-76\) \(+\) \(+\)
8033.2.a.c \(154\) \(64.144\) None \(-12\) \(-36\) \(-9\) \(-68\) \(-\) \(-\)
8033.2.a.d \(168\) \(64.144\) None \(12\) \(35\) \(12\) \(74\) \(-\) \(+\)
8033.2.a.e \(169\) \(64.144\) None \(3\) \(8\) \(13\) \(76\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8033))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8033)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(277))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - T + 2 T^{2} \))
$3$ (\( 1 - T + 3 T^{2} \))
$5$ (\( 1 + 3 T + 5 T^{2} \))
$7$ (\( 1 - 2 T + 7 T^{2} \))
$11$ (\( 1 + 3 T + 11 T^{2} \))
$13$ (\( 1 - T + 13 T^{2} \))
$17$ (\( 1 + 2 T + 17 T^{2} \))
$19$ (\( 1 + 4 T + 19 T^{2} \))
$23$ (\( 1 + 4 T + 23 T^{2} \))
$29$ (\( 1 - T \))
$31$ (\( 1 + 9 T + 31 T^{2} \))
$37$ (\( 1 - 8 T + 37 T^{2} \))
$41$ (\( 1 + 6 T + 41 T^{2} \))
$43$ (\( 1 - 13 T + 43 T^{2} \))
$47$ (\( 1 + 7 T + 47 T^{2} \))
$53$ (\( 1 - 9 T + 53 T^{2} \))
$59$ (\( 1 + 59 T^{2} \))
$61$ (\( 1 - 4 T + 61 T^{2} \))
$67$ (\( 1 - 2 T + 67 T^{2} \))
$71$ (\( 1 + 12 T + 71 T^{2} \))
$73$ (\( 1 - 14 T + 73 T^{2} \))
$79$ (\( 1 - 3 T + 79 T^{2} \))
$83$ (\( 1 - 10 T + 83 T^{2} \))
$89$ (\( 1 + 12 T + 89 T^{2} \))
$97$ (\( 1 - 14 T + 97 T^{2} \))
show more
show less