Properties

Label 8019.2.a
Level 8019
Weight 2
Character orbit a
Rep. character \(\chi_{8019}(1,\cdot)\)
Character field \(\Q\)
Dimension 360
Newform subspaces 12
Sturm bound 1944
Trace bound 5

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Defining parameters

Level: \( N \) = \( 8019 = 3^{6} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8019.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(1944\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8019))\).

Total New Old
Modular forms 1008 360 648
Cusp forms 937 360 577
Eisenstein series 71 0 71

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

\(3\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(87\)
\(+\)\(-\)\(-\)\(99\)
\(-\)\(+\)\(-\)\(93\)
\(-\)\(-\)\(+\)\(81\)
Plus space\(+\)\(168\)
Minus space\(-\)\(192\)

Trace form

\( 360q + 360q^{4} + O(q^{10}) \) \( 360q + 360q^{4} + 360q^{16} + 360q^{25} + 360q^{49} - 36q^{61} + 360q^{64} - 36q^{67} - 36q^{73} + 108q^{82} + 108q^{85} - 36q^{91} + 108q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8019))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 11
8019.2.a.a \(3\) \(64.032\) \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(-3\) \(-3\) \(+\) \(+\) \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}-2\beta _{2})q^{5}+\cdots\)
8019.2.a.b \(3\) \(64.032\) \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(3\) \(-3\) \(-\) \(-\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{1}+2\beta _{2})q^{5}+\cdots\)
8019.2.a.c \(21\) \(64.032\) None \(-6\) \(0\) \(-12\) \(0\) \(-\) \(-\)
8019.2.a.d \(21\) \(64.032\) None \(0\) \(0\) \(-12\) \(0\) \(-\) \(-\)
8019.2.a.e \(21\) \(64.032\) None \(0\) \(0\) \(12\) \(0\) \(-\) \(+\)
8019.2.a.f \(21\) \(64.032\) None \(6\) \(0\) \(12\) \(0\) \(-\) \(+\)
8019.2.a.g \(36\) \(64.032\) None \(0\) \(0\) \(-9\) \(-9\) \(-\) \(-\)
8019.2.a.h \(36\) \(64.032\) None \(0\) \(0\) \(9\) \(-9\) \(+\) \(+\)
8019.2.a.i \(48\) \(64.032\) None \(-6\) \(0\) \(-24\) \(0\) \(+\) \(+\)
8019.2.a.j \(48\) \(64.032\) None \(6\) \(0\) \(24\) \(0\) \(+\) \(-\)
8019.2.a.k \(51\) \(64.032\) None \(0\) \(0\) \(-6\) \(12\) \(-\) \(+\)
8019.2.a.l \(51\) \(64.032\) None \(0\) \(0\) \(6\) \(12\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8019))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8019)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(243))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(297))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(729))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(891))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2673))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 3 T^{2} + T^{3} + 6 T^{4} + 8 T^{6} \))(\( 1 + 3 T^{2} - T^{3} + 6 T^{4} + 8 T^{6} \))
$3$ 1
$5$ (\( 1 + 3 T + 9 T^{2} + 13 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6} \))(\( 1 - 3 T + 9 T^{2} - 13 T^{3} + 45 T^{4} - 75 T^{5} + 125 T^{6} \))
$7$ (\( 1 + 3 T + 21 T^{2} + 41 T^{3} + 147 T^{4} + 147 T^{5} + 343 T^{6} \))(\( 1 + 3 T + 21 T^{2} + 41 T^{3} + 147 T^{4} + 147 T^{5} + 343 T^{6} \))
$11$ (\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))
$13$ (\( 1 + 9 T + 45 T^{2} + 161 T^{3} + 585 T^{4} + 1521 T^{5} + 2197 T^{6} \))(\( 1 + 9 T + 45 T^{2} + 161 T^{3} + 585 T^{4} + 1521 T^{5} + 2197 T^{6} \))
$17$ (\( 1 - 12 T + 96 T^{2} - 461 T^{3} + 1632 T^{4} - 3468 T^{5} + 4913 T^{6} \))(\( 1 + 12 T + 96 T^{2} + 461 T^{3} + 1632 T^{4} + 3468 T^{5} + 4913 T^{6} \))
$19$ (\( 1 - 12 T + 84 T^{2} - 399 T^{3} + 1596 T^{4} - 4332 T^{5} + 6859 T^{6} \))(\( 1 - 12 T + 84 T^{2} - 399 T^{3} + 1596 T^{4} - 4332 T^{5} + 6859 T^{6} \))
$23$ (\( 1 + 57 T^{2} + 8 T^{3} + 1311 T^{4} + 12167 T^{6} \))(\( 1 + 57 T^{2} - 8 T^{3} + 1311 T^{4} + 12167 T^{6} \))
$29$ (\( 1 - 6 T + 15 T^{2} + 108 T^{3} + 435 T^{4} - 5046 T^{5} + 24389 T^{6} \))(\( 1 + 6 T + 15 T^{2} - 108 T^{3} + 435 T^{4} + 5046 T^{5} + 24389 T^{6} \))
$31$ (\( 1 - 3 T + 60 T^{2} - 223 T^{3} + 1860 T^{4} - 2883 T^{5} + 29791 T^{6} \))(\( 1 - 3 T + 60 T^{2} - 223 T^{3} + 1860 T^{4} - 2883 T^{5} + 29791 T^{6} \))
$37$ (\( 1 + 75 T^{2} - 72 T^{3} + 2775 T^{4} + 50653 T^{6} \))(\( 1 + 75 T^{2} - 72 T^{3} + 2775 T^{4} + 50653 T^{6} \))
$41$ (\( 1 - 3 T + 87 T^{2} - 227 T^{3} + 3567 T^{4} - 5043 T^{5} + 68921 T^{6} \))(\( 1 + 3 T + 87 T^{2} + 227 T^{3} + 3567 T^{4} + 5043 T^{5} + 68921 T^{6} \))
$43$ (\( 1 + 3 T + 48 T^{2} + 471 T^{3} + 2064 T^{4} + 5547 T^{5} + 79507 T^{6} \))(\( 1 + 3 T + 48 T^{2} + 471 T^{3} + 2064 T^{4} + 5547 T^{5} + 79507 T^{6} \))
$47$ (\( 1 - 15 T + 195 T^{2} - 1393 T^{3} + 9165 T^{4} - 33135 T^{5} + 103823 T^{6} \))(\( 1 + 15 T + 195 T^{2} + 1393 T^{3} + 9165 T^{4} + 33135 T^{5} + 103823 T^{6} \))
$53$ (\( 1 + 21 T + 294 T^{2} + 2493 T^{3} + 15582 T^{4} + 58989 T^{5} + 148877 T^{6} \))(\( 1 - 21 T + 294 T^{2} - 2493 T^{3} + 15582 T^{4} - 58989 T^{5} + 148877 T^{6} \))
$59$ (\( 1 - 9 T + 192 T^{2} - 1045 T^{3} + 11328 T^{4} - 31329 T^{5} + 205379 T^{6} \))(\( 1 + 9 T + 192 T^{2} + 1045 T^{3} + 11328 T^{4} + 31329 T^{5} + 205379 T^{6} \))
$61$ (\( 1 + 6 T + 183 T^{2} + 708 T^{3} + 11163 T^{4} + 22326 T^{5} + 226981 T^{6} \))(\( 1 + 6 T + 183 T^{2} + 708 T^{3} + 11163 T^{4} + 22326 T^{5} + 226981 T^{6} \))
$67$ (\( 1 + 3 T + 33 T^{2} - 425 T^{3} + 2211 T^{4} + 13467 T^{5} + 300763 T^{6} \))(\( 1 + 3 T + 33 T^{2} - 425 T^{3} + 2211 T^{4} + 13467 T^{5} + 300763 T^{6} \))
$71$ (\( 1 - 21 T + 267 T^{2} - 2385 T^{3} + 18957 T^{4} - 105861 T^{5} + 357911 T^{6} \))(\( 1 + 21 T + 267 T^{2} + 2385 T^{3} + 18957 T^{4} + 105861 T^{5} + 357911 T^{6} \))
$73$ (\( 1 - 3 T + 105 T^{2} - 169 T^{3} + 7665 T^{4} - 15987 T^{5} + 389017 T^{6} \))(\( 1 - 3 T + 105 T^{2} - 169 T^{3} + 7665 T^{4} - 15987 T^{5} + 389017 T^{6} \))
$79$ (\( 1 + 21 T + 321 T^{2} + 3049 T^{3} + 25359 T^{4} + 131061 T^{5} + 493039 T^{6} \))(\( 1 + 21 T + 321 T^{2} + 3049 T^{3} + 25359 T^{4} + 131061 T^{5} + 493039 T^{6} \))
$83$ (\( 1 - 3 T + 69 T^{2} + 585 T^{3} + 5727 T^{4} - 20667 T^{5} + 571787 T^{6} \))(\( 1 + 3 T + 69 T^{2} - 585 T^{3} + 5727 T^{4} + 20667 T^{5} + 571787 T^{6} \))
$89$ (\( 1 - 18 T + 186 T^{2} - 1827 T^{3} + 16554 T^{4} - 142578 T^{5} + 704969 T^{6} \))(\( 1 + 18 T + 186 T^{2} + 1827 T^{3} + 16554 T^{4} + 142578 T^{5} + 704969 T^{6} \))
$97$ (\( 1 - 27 T + 450 T^{2} - 5075 T^{3} + 43650 T^{4} - 254043 T^{5} + 912673 T^{6} \))(\( 1 - 27 T + 450 T^{2} - 5075 T^{3} + 43650 T^{4} - 254043 T^{5} + 912673 T^{6} \))
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