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 $4$

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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

\( 8q - 32q^{4} - 44q^{7} + O(q^{10}) \) \( 8q - 32q^{4} - 44q^{7} + 188q^{16} - 996q^{22} + 776q^{25} + 980q^{28} - 736q^{37} - 760q^{43} + 132q^{46} + 968q^{49} - 1164q^{58} - 5600q^{64} + 4144q^{67} + 3552q^{70} - 2192q^{79} - 5328q^{85} + 6852q^{88} + 1776q^{91} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
63.4.c.a \(4\) \(3.717\) \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-8-5\beta _{3})q^{4}-7\beta _{3}q^{7}+\cdots\)
63.4.c.b \(4\) \(3.717\) \(\Q(\sqrt{-2}, \sqrt{111})\) None \(0\) \(0\) \(0\) \(-44\) \(q+2\beta _{1}q^{2}+\beta _{3}q^{5}+(-11-\beta _{2})q^{7}+\cdots\)

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

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