Properties

Label 384.4.c
Level $384$
Weight $4$
Character orbit 384.c
Rep. character $\chi_{384}(383,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $4$
Sturm bound $256$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 384.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(256\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(384, [\chi])\).

Total New Old
Modular forms 208 48 160
Cusp forms 176 48 128
Eisenstein series 32 0 32

Trace form

\( 48 q + O(q^{10}) \) \( 48 q - 1200 q^{25} - 464 q^{33} - 3792 q^{49} - 688 q^{57} - 864 q^{73} - 4304 q^{81} - 192 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(384, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
384.4.c.a 384.c 12.b $12$ $22.657$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{5})q^{3}+\beta _{1}q^{5}-\beta _{2}q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots\)
384.4.c.b 384.c 12.b $12$ $22.657$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{6})q^{3}+\beta _{1}q^{5}-\beta _{2}q^{7}+(\beta _{2}+\cdots)q^{9}+\cdots\)
384.4.c.c 384.c 12.b $12$ $22.657$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{6})q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}+(\beta _{2}+\cdots)q^{9}+\cdots\)
384.4.c.d 384.c 12.b $12$ $22.657$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{5})q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)