Properties

Label 35.2.j
Level 35
Weight 2
Character orbit j
Rep. character \(\chi_{35}(4,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 4
Newform subspaces 1
Sturm bound 8
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 35 = 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 35.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(35, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

Trace form

\( 4q - 2q^{4} - 2q^{5} - 4q^{6} - 4q^{9} + O(q^{10}) \) \( 4q - 2q^{4} - 2q^{5} - 4q^{6} - 4q^{9} - 4q^{10} + 8q^{14} + 8q^{15} + 2q^{16} + 12q^{19} + 4q^{20} - 10q^{21} + 6q^{24} + 6q^{25} - 4q^{26} - 28q^{29} + 2q^{30} - 4q^{31} - 8q^{34} - 16q^{35} + 8q^{36} - 4q^{39} - 12q^{40} + 20q^{41} - 4q^{45} + 6q^{46} + 26q^{49} + 16q^{50} + 4q^{51} + 10q^{54} + 6q^{56} + 20q^{59} - 4q^{60} - 14q^{61} - 28q^{64} + 8q^{65} - 12q^{69} - 10q^{70} - 8q^{71} - 16q^{74} - 8q^{75} - 24q^{76} - 4q^{79} + 2q^{80} - 2q^{81} + 8q^{84} + 16q^{85} - 14q^{86} + 18q^{89} + 16q^{90} - 4q^{91} + 12q^{95} + 10q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
35.2.j.a \(4\) \(0.279\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 3 T^{2} + 5 T^{4} + 12 T^{6} + 16 T^{8} \)
$3$ \( 1 + 5 T^{2} + 16 T^{4} + 45 T^{6} + 81 T^{8} \)
$5$ \( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \)
$7$ \( 1 - 13 T^{2} + 49 T^{4} \)
$11$ \( ( 1 - 11 T^{2} + 121 T^{4} )^{2} \)
$13$ \( ( 1 - 22 T^{2} + 169 T^{4} )^{2} \)
$17$ \( ( 1 - 8 T + 47 T^{2} - 136 T^{3} + 289 T^{4} )( 1 + 8 T + 47 T^{2} + 136 T^{3} + 289 T^{4} ) \)
$19$ \( ( 1 - 6 T + 17 T^{2} - 114 T^{3} + 361 T^{4} )^{2} \)
$23$ \( 1 + 37 T^{2} + 840 T^{4} + 19573 T^{6} + 279841 T^{8} \)
$29$ \( ( 1 + 7 T + 29 T^{2} )^{4} \)
$31$ \( ( 1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4} )^{2} \)
$37$ \( 1 + 10 T^{2} - 1269 T^{4} + 13690 T^{6} + 1874161 T^{8} \)
$41$ \( ( 1 - 5 T + 41 T^{2} )^{4} \)
$43$ \( ( 1 - 37 T^{2} + 1849 T^{4} )^{2} \)
$47$ \( ( 1 + 47 T^{2} + 2209 T^{4} )^{2} \)
$53$ \( 1 + 70 T^{2} + 2091 T^{4} + 196630 T^{6} + 7890481 T^{8} \)
$59$ \( ( 1 - 10 T + 41 T^{2} - 590 T^{3} + 3481 T^{4} )^{2} \)
$61$ \( ( 1 + 7 T - 12 T^{2} + 427 T^{3} + 3721 T^{4} )^{2} \)
$67$ \( ( 1 - 13 T^{2} + 4489 T^{4} )( 1 + 122 T^{2} + 4489 T^{4} ) \)
$71$ \( ( 1 + 2 T + 71 T^{2} )^{4} \)
$73$ \( ( 1 - 16 T + 183 T^{2} - 1168 T^{3} + 5329 T^{4} )( 1 + 16 T + 183 T^{2} + 1168 T^{3} + 5329 T^{4} ) \)
$79$ \( ( 1 + 2 T - 75 T^{2} + 158 T^{3} + 6241 T^{4} )^{2} \)
$83$ \( ( 1 - 45 T^{2} + 6889 T^{4} )^{2} \)
$89$ \( ( 1 - 9 T - 8 T^{2} - 801 T^{3} + 7921 T^{4} )^{2} \)
$97$ \( ( 1 + 62 T^{2} + 9409 T^{4} )^{2} \)
show more
show less