Properties

Label 63.2.c
Level $63$
Weight $2$
Character orbit 63.c
Rep. character $\chi_{63}(62,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 63.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(63, [\chi])\).

Total New Old
Modular forms 12 4 8
Cusp forms 4 4 0
Eisenstein series 8 0 8

Trace form

\( 4q - 8q^{4} + O(q^{10}) \) \( 4q - 8q^{4} + 12q^{16} + 20q^{22} - 20q^{25} - 28q^{28} + 44q^{46} + 28q^{49} - 52q^{58} - 24q^{64} - 16q^{67} + 32q^{79} + 28q^{88} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(63, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
63.2.c.a \(4\) \(0.503\) \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{2}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)