Properties

Label 252.2.t
Level 252
Weight 2
Character orbit t
Rep. character \(\chi_{252}(17,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 4
Newform subspaces 1
Sturm bound 96
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 252.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(252, [\chi])\).

Total New Old
Modular forms 120 4 116
Cusp forms 72 4 68
Eisenstein series 48 0 48

Trace form

\( 4q + 2q^{7} + O(q^{10}) \) \( 4q + 2q^{7} + 18q^{19} - 2q^{25} - 6q^{31} + 10q^{37} - 44q^{43} - 26q^{49} - 12q^{61} + 14q^{67} + 54q^{73} - 22q^{79} - 48q^{85} + 18q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
252.2.t.a \(4\) \(2.012\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(2\) \(q-\beta _{2}q^{5}+(2-3\beta _{1})q^{7}+(-\beta _{2}-\beta _{3})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ \( 1 - 4 T^{2} - 9 T^{4} - 100 T^{6} + 625 T^{8} \)
$7$ \( ( 1 - T + 7 T^{2} )^{2} \)
$11$ \( 1 + 4 T^{2} - 105 T^{4} + 484 T^{6} + 14641 T^{8} \)
$13$ \( ( 1 - 7 T + 13 T^{2} )^{2}( 1 + 7 T + 13 T^{2} )^{2} \)
$17$ \( 1 - 10 T^{2} - 189 T^{4} - 2890 T^{6} + 83521 T^{8} \)
$19$ \( ( 1 - 8 T + 19 T^{2} )^{2}( 1 - T + 19 T^{2} )^{2} \)
$23$ \( ( 1 + 23 T^{2} + 529 T^{4} )^{2} \)
$29$ \( ( 1 + 14 T^{2} + 841 T^{4} )^{2} \)
$31$ \( ( 1 - 4 T + 31 T^{2} )^{2}( 1 + 7 T + 31 T^{2} )^{2} \)
$37$ \( ( 1 - 5 T - 12 T^{2} - 185 T^{3} + 1369 T^{4} )^{2} \)
$41$ \( ( 1 - 68 T^{2} + 1681 T^{4} )^{2} \)
$43$ \( ( 1 + 11 T + 43 T^{2} )^{4} \)
$47$ \( 1 - 88 T^{2} + 5535 T^{4} - 194392 T^{6} + 4879681 T^{8} \)
$53$ \( 1 + 34 T^{2} - 1653 T^{4} + 95506 T^{6} + 7890481 T^{8} \)
$59$ \( 1 - 94 T^{2} + 5355 T^{4} - 327214 T^{6} + 12117361 T^{8} \)
$61$ \( ( 1 + 6 T + 73 T^{2} + 366 T^{3} + 3721 T^{4} )^{2} \)
$67$ \( ( 1 - 7 T - 18 T^{2} - 469 T^{3} + 4489 T^{4} )^{2} \)
$71$ \( ( 1 + 20 T^{2} + 5041 T^{4} )^{2} \)
$73$ \( ( 1 - 17 T + 73 T^{2} )^{2}( 1 - 10 T + 73 T^{2} )^{2} \)
$79$ \( ( 1 + 11 T + 42 T^{2} + 869 T^{3} + 6241 T^{4} )^{2} \)
$83$ \( ( 1 + 16 T^{2} + 6889 T^{4} )^{2} \)
$89$ \( 1 + 38 T^{2} - 6477 T^{4} + 300998 T^{6} + 62742241 T^{8} \)
$97$ \( ( 1 - 182 T^{2} + 9409 T^{4} )^{2} \)
show more
show less