Properties

Label 128.8.b
Level $128$
Weight $8$
Character orbit 128.b
Rep. character $\chi_{128}(65,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $7$
Sturm bound $128$
Trace bound $9$

Related objects

Downloads

Learn more

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(128, [\chi])\).

Total New Old
Modular forms 120 28 92
Cusp forms 104 28 76
Eisenstein series 16 0 16

Trace form

\( 28 q - 20412 q^{9} + O(q^{10}) \) \( 28 q - 20412 q^{9} + 5816 q^{17} - 469748 q^{25} + 198032 q^{33} + 2084984 q^{41} + 5338364 q^{49} + 4831696 q^{57} - 6374176 q^{65} - 2987656 q^{73} + 16222156 q^{81} - 29572040 q^{89} + 56441208 q^{97} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(128, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
128.8.b.a 128.b 8.b $2$ $39.985$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+13\beta q^{3}+835q^{9}+181\beta q^{11}+22182q^{17}+\cdots\)
128.8.b.b 128.b 8.b $2$ $39.985$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-139iq^{5}+3^{7}q^{9}-3277iq^{13}+\cdots\)
128.8.b.c 128.b 8.b $4$ $39.985$ \(\Q(\sqrt{2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+\beta _{3}q^{5}+71\beta _{1}q^{7}-4573q^{9}+\cdots\)
128.8.b.d 128.b 8.b $4$ $39.985$ \(\Q(\sqrt{-2}, \sqrt{-85})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+21\beta _{1}q^{3}+\beta _{3}q^{5}-\beta _{2}q^{7}-1341q^{9}+\cdots\)
128.8.b.e 128.b 8.b $4$ $39.985$ \(\Q(i, \sqrt{46})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+45\beta _{1}q^{5}+\beta _{3}q^{7}-757q^{9}+\cdots\)
128.8.b.f 128.b 8.b $4$ $39.985$ \(\Q(\sqrt{2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\beta _{1}q^{3}+17\beta _{3}q^{5}-29\beta _{2}q^{7}+1827q^{9}+\cdots\)
128.8.b.g 128.b 8.b $8$ $39.985$ 8.0.\(\cdots\).13 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+\beta _{5}q^{7}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(128, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)