Properties

Label 384.4.f
Level $384$
Weight $4$
Character orbit 384.f
Rep. character $\chi_{384}(191,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $9$
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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(256\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(5\), \(23\)

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

\( 48 q + O(q^{10}) \) \( 48 q + 1200 q^{25} - 464 q^{33} - 912 q^{49} + 688 q^{57} - 864 q^{73} + 624 q^{81} + 6144 q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
384.4.f.a $4$ $22.657$ \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}-7\beta _{1}q^{5}-\beta _{3}q^{7}-3^{3}q^{9}+\cdots\)
384.4.f.b $4$ $22.657$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{3}+(-23+5\zeta_{8})q^{9}+(3\zeta_{8}^{2}+\cdots)q^{11}+\cdots\)
384.4.f.c $4$ $22.657$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}+2\zeta_{8}^{2})q^{3}-2\zeta_{8}^{2}q^{5}+2\zeta_{8}^{3}q^{7}+\cdots\)
384.4.f.d $4$ $22.657$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-2\zeta_{8}^{2})q^{3}-2\zeta_{8}^{2}q^{5}-2\zeta_{8}^{3}q^{7}+\cdots\)
384.4.f.e $4$ $22.657$ \(\Q(i, \sqrt{26})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+2\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\)
384.4.f.f $4$ $22.657$ \(\Q(i, \sqrt{26})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+(\beta _{1}+2\beta _{2})q^{5}+\beta _{3}q^{7}+(5^{2}+\cdots)q^{9}+\cdots\)
384.4.f.g $8$ $22.657$ 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}+\beta _{4})q^{3}+(-2\beta _{3}+\beta _{6})q^{5}+(-3\beta _{2}+\cdots)q^{7}+\cdots\)
384.4.f.h $8$ $22.657$ 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{3}+(-2\beta _{3}+\beta _{6})q^{5}+(-3\beta _{2}+\cdots)q^{7}+\cdots\)
384.4.f.i $8$ $22.657$ 8.0.\(\cdots\).6 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{5}+\beta _{7}q^{7}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)