↑

Properties

Label 63.8.c
Level $63$
Weight $8$
Character orbit 63.c
Rep. character $\chi_{63}(62,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $2$
Sturm bound $64$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 63.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(64\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(63, [\chi])\).

Total New Old
Modular forms 60 20 40
Cusp forms 52 20 32
Eisenstein series 8 0 8

Trace form

\( 20 q - 1536 q^{4} + 2240 q^{7} + 141628 q^{16} - 123940 q^{22} + 367196 q^{25} - 365484 q^{28} + 1881760 q^{37} - 2301440 q^{43} + 1619588 q^{46} - 2339092 q^{49} + 13571924 q^{58} - 19265536 q^{64} + 12462448 q^{67}+ \cdots + 30119712 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(63, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.8.c.a 63.c 21.c $4$ $19.680$ \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) 63.8.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-2\beta _{1}+\beta _{2})q^{2}+(-2^{7}+13\beta _{3})q^{4}+\cdots\)
63.8.c.b 63.c 21.c $16$ $19.680$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 63.8.c.b \(0\) \(0\) \(0\) \(2240\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-2^{6}-\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(63, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)