Properties

Label 384.4.d
Level $384$
Weight $4$
Character orbit 384.d
Rep. character $\chi_{384}(193,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $6$
Sturm bound $256$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 384.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(256\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 208 24 184
Cusp forms 176 24 152
Eisenstein series 32 0 32

Trace form

\( 24 q - 216 q^{9} + O(q^{10}) \) \( 24 q - 216 q^{9} + 208 q^{17} - 424 q^{25} + 944 q^{41} - 264 q^{49} + 672 q^{57} + 832 q^{65} - 2640 q^{73} + 1944 q^{81} + 528 q^{89} - 3440 q^{97} + O(q^{100}) \)

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.d.a $2$ $22.657$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-24\) \(q-3iq^{3}+8iq^{5}-12q^{7}-9q^{9}-12iq^{11}+\cdots\)
384.4.d.b $2$ $22.657$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(24\) \(q+3iq^{3}+8iq^{5}+12q^{7}-9q^{9}+12iq^{11}+\cdots\)
384.4.d.c $4$ $22.657$ \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(-32\) \(q-3\beta _{1}q^{3}+(-4\beta _{1}+\beta _{2})q^{5}+(-8+\cdots)q^{7}+\cdots\)
384.4.d.d $4$ $22.657$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+3\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}-5\zeta_{8}^{3}q^{7}-9q^{9}+\cdots\)
384.4.d.e $4$ $22.657$ \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(32\) \(q+3\beta _{1}q^{3}+(-4\beta _{1}+\beta _{2})q^{5}+(8-\beta _{3})q^{7}+\cdots\)
384.4.d.f $8$ $22.657$ 8.0.1534132224.8 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{6}q^{5}-\beta _{2}q^{7}-9q^{9}+(-4\beta _{1}+\cdots)q^{11}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)