Properties

Label 128.2.b
Level $128$
Weight $2$
Character orbit 128.b
Rep. character $\chi_{128}(65,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $32$
Trace bound $9$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 128.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(128, [\chi])\).

Total New Old
Modular forms 24 4 20
Cusp forms 8 4 4
Eisenstein series 16 0 16

Trace form

\( 4q - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{9} + 8q^{17} - 12q^{25} - 16q^{33} + 8q^{41} - 28q^{49} + 48q^{57} + 32q^{65} + 8q^{73} + 20q^{81} - 56q^{89} - 56q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(128, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
128.2.b.a \(2\) \(1.022\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{3}-5q^{9}+\beta q^{11}+6q^{17}-3\beta q^{19}+\cdots\)
128.2.b.b \(2\) \(1.022\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}+3q^{9}-iq^{13}-2q^{17}-11q^{25}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(128, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( ( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} ) \))(\( ( 1 - 3 T^{2} )^{2} \))
$5$ (\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} ) \))
$7$ (\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))
$11$ (\( ( 1 - 6 T + 11 T^{2} )( 1 + 6 T + 11 T^{2} ) \))(\( ( 1 - 11 T^{2} )^{2} \))
$13$ (\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))
$17$ (\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))
$19$ (\( ( 1 - 2 T + 19 T^{2} )( 1 + 2 T + 19 T^{2} ) \))(\( ( 1 - 19 T^{2} )^{2} \))
$23$ (\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))
$29$ (\( ( 1 - 29 T^{2} )^{2} \))(\( ( 1 - 10 T + 29 T^{2} )( 1 + 10 T + 29 T^{2} ) \))
$31$ (\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))
$37$ (\( ( 1 - 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )( 1 + 2 T + 37 T^{2} ) \))
$41$ (\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))
$43$ (\( ( 1 - 10 T + 43 T^{2} )( 1 + 10 T + 43 T^{2} ) \))(\( ( 1 - 43 T^{2} )^{2} \))
$47$ (\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))
$53$ (\( ( 1 - 53 T^{2} )^{2} \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))
$59$ (\( ( 1 - 6 T + 59 T^{2} )( 1 + 6 T + 59 T^{2} ) \))(\( ( 1 - 59 T^{2} )^{2} \))
$61$ (\( ( 1 - 61 T^{2} )^{2} \))(\( ( 1 - 10 T + 61 T^{2} )( 1 + 10 T + 61 T^{2} ) \))
$67$ (\( ( 1 - 14 T + 67 T^{2} )( 1 + 14 T + 67 T^{2} ) \))(\( ( 1 - 67 T^{2} )^{2} \))
$71$ (\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))
$73$ (\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 - 6 T + 73 T^{2} )^{2} \))
$79$ (\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))
$83$ (\( ( 1 - 18 T + 83 T^{2} )( 1 + 18 T + 83 T^{2} ) \))(\( ( 1 - 83 T^{2} )^{2} \))
$89$ (\( ( 1 + 18 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))
$97$ (\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 18 T + 97 T^{2} )^{2} \))
show more
show less