↑

Properties

Label 63.4.c
Level $63$
Weight $4$
Character orbit 63.c
Rep. character $\chi_{63}(62,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $32$
Trace bound $4$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(32\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(63, [\chi])\).

Total New Old
Modular forms 28 8 20
Cusp forms 20 8 12
Eisenstein series 8 0 8

Trace form

\( 8 q - 32 q^{4} - 44 q^{7} + 188 q^{16} - 996 q^{22} + 776 q^{25} + 980 q^{28} - 736 q^{37} - 760 q^{43} + 132 q^{46} + 968 q^{49} - 1164 q^{58} - 5600 q^{64} + 4144 q^{67} + 3552 q^{70} - 2192 q^{79} - 5328 q^{85}+ \cdots + 1776 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(63, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.4.c.a 63.c 21.c $4$ $3.717$ \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) 63.4.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{2}+(-8-5\beta _{3})q^{4}-7\beta _{3}q^{7}+\cdots\)
63.4.c.b 63.c 21.c $4$ $3.717$ \(\Q(\sqrt{-2}, \sqrt{111})\) None 63.4.c.b \(0\) \(0\) \(0\) \(-44\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta _{1}q^{2}+\beta _{3}q^{5}+(-11-\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(63, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)