Properties

Label 1024.2.g
Level $1024$
Weight $2$
Character orbit 1024.g
Rep. character $\chi_{1024}(129,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $128$
Newform subspaces $8$
Sturm bound $256$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1024 = 2^{10} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1024.g (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 8 \)
Sturm bound: \(256\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1024, [\chi])\).

Total New Old
Modular forms 608 128 480
Cusp forms 416 128 288
Eisenstein series 192 0 192

Trace form

\( 128 q + O(q^{10}) \) \( 128 q + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1024, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1024.2.g.a 1024.g 32.g $16$ $8.177$ \(\Q(\zeta_{48})\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\zeta_{48}^{15}q^{3}+(-1+\zeta_{48}^{3}-\zeta_{48}^{8}+\cdots)q^{5}+\cdots\)
1024.2.g.b 1024.g 32.g $16$ $8.177$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\beta _{2}q^{3}+(\beta _{3}+\beta _{10})q^{5}+(-\beta _{4}-\beta _{9}+\cdots)q^{7}+\cdots\)
1024.2.g.c 1024.g 32.g $16$ $8.177$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\beta _{13}q^{3}+(-1-\beta _{3}+\beta _{5}+\beta _{8})q^{5}+\cdots\)
1024.2.g.d 1024.g 32.g $16$ $8.177$ \(\Q(\zeta_{48})\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+(\zeta_{48}^{11}+\zeta_{48}^{14})q^{3}+(-\zeta_{48}-\zeta_{48}^{2}+\cdots)q^{5}+\cdots\)
1024.2.g.e 1024.g 32.g $16$ $8.177$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\beta _{2}q^{3}+(-\beta _{3}-\beta _{10})q^{5}+(\beta _{4}+\beta _{9}+\cdots)q^{7}+\cdots\)
1024.2.g.f 1024.g 32.g $16$ $8.177$ \(\Q(\zeta_{48})\) None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\zeta_{48}^{15}q^{3}+(1+\zeta_{48}^{8}+\zeta_{48}^{13}+\cdots)q^{5}+\cdots\)
1024.2.g.g 1024.g 32.g $16$ $8.177$ \(\Q(\zeta_{48})\) None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+(\zeta_{48}^{11}+\zeta_{48}^{14})q^{3}+(\zeta_{48}+\zeta_{48}^{2}+\cdots)q^{5}+\cdots\)
1024.2.g.h 1024.g 32.g $16$ $8.177$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\beta _{13}q^{3}+(1+\beta _{3}-\beta _{5}-\beta _{8})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1024, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(512, [\chi])\)\(^{\oplus 2}\)