Properties

Label 37.2.c
Level 37
Weight 2
Character orbit c
Rep. character \(\chi_{37}(10,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 2
Newform subspaces 1
Sturm bound 6
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 37.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(37, [\chi])\).

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

Trace form

\( 2q - q^{2} + q^{4} - q^{5} - 2q^{7} - 6q^{8} + 3q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{4} - q^{5} - 2q^{7} - 6q^{8} + 3q^{9} + 2q^{10} - 4q^{11} + 2q^{13} + 4q^{14} + q^{16} - 3q^{17} + 3q^{18} + 6q^{19} + q^{20} + 2q^{22} - 8q^{23} + 4q^{25} - 4q^{26} + 2q^{28} + 18q^{29} - 20q^{31} - 5q^{32} - 3q^{34} - 2q^{35} + 6q^{36} - 11q^{37} - 12q^{38} + 3q^{40} + 9q^{41} + 4q^{43} - 2q^{44} - 6q^{45} + 4q^{46} + 12q^{47} + 3q^{49} + 4q^{50} - 2q^{52} + 2q^{53} + 2q^{55} + 6q^{56} - 9q^{58} + 4q^{59} - q^{61} + 10q^{62} - 12q^{63} + 14q^{64} + 2q^{65} + 10q^{67} - 6q^{68} - 2q^{70} - 6q^{71} - 9q^{72} - 20q^{73} + 10q^{74} - 6q^{76} + 4q^{77} - 10q^{79} - 2q^{80} - 9q^{81} - 18q^{82} + 12q^{83} + 6q^{85} - 2q^{86} + 12q^{88} - 7q^{89} + 3q^{90} + 4q^{91} - 4q^{92} - 6q^{94} + 6q^{95} + 14q^{97} + 3q^{98} - 6q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(37, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
37.2.c.a \(2\) \(0.295\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}-2\zeta_{6}q^{7}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T - T^{2} + 2 T^{3} + 4 T^{4} \)
$3$ \( ( 1 - 3 T + 3 T^{2} )( 1 + 3 T + 3 T^{2} ) \)
$5$ \( 1 + T - 4 T^{2} + 5 T^{3} + 25 T^{4} \)
$7$ \( 1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4} \)
$11$ \( ( 1 + 2 T + 11 T^{2} )^{2} \)
$13$ \( ( 1 - 7 T + 13 T^{2} )( 1 + 5 T + 13 T^{2} ) \)
$17$ \( 1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4} \)
$19$ \( 1 - 6 T + 17 T^{2} - 114 T^{3} + 361 T^{4} \)
$23$ \( ( 1 + 4 T + 23 T^{2} )^{2} \)
$29$ \( ( 1 - 9 T + 29 T^{2} )^{2} \)
$31$ \( ( 1 + 10 T + 31 T^{2} )^{2} \)
$37$ \( 1 + 11 T + 37 T^{2} \)
$41$ \( 1 - 9 T + 40 T^{2} - 369 T^{3} + 1681 T^{4} \)
$43$ \( ( 1 - 2 T + 43 T^{2} )^{2} \)
$47$ \( ( 1 - 6 T + 47 T^{2} )^{2} \)
$53$ \( 1 - 2 T - 49 T^{2} - 106 T^{3} + 2809 T^{4} \)
$59$ \( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} \)
$61$ \( ( 1 - 13 T + 61 T^{2} )( 1 + 14 T + 61 T^{2} ) \)
$67$ \( 1 - 10 T + 33 T^{2} - 670 T^{3} + 4489 T^{4} \)
$71$ \( 1 + 6 T - 35 T^{2} + 426 T^{3} + 5041 T^{4} \)
$73$ \( ( 1 + 10 T + 73 T^{2} )^{2} \)
$79$ \( 1 + 10 T + 21 T^{2} + 790 T^{3} + 6241 T^{4} \)
$83$ \( 1 - 12 T + 61 T^{2} - 996 T^{3} + 6889 T^{4} \)
$89$ \( 1 + 7 T - 40 T^{2} + 623 T^{3} + 7921 T^{4} \)
$97$ \( ( 1 - 7 T + 97 T^{2} )^{2} \)
show more
show less