Properties

Label 384.2.d
Level $384$
Weight $2$
Character orbit 384.d
Rep. character $\chi_{384}(193,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $3$
Sturm bound $128$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(128\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(384, [\chi])\).

Total New Old
Modular forms 80 8 72
Cusp forms 48 8 40
Eisenstein series 32 0 32

Trace form

\( 8q - 8q^{9} + O(q^{10}) \) \( 8q - 8q^{9} - 16q^{17} + 8q^{25} + 16q^{41} + 40q^{49} - 32q^{57} - 64q^{65} + 16q^{73} + 8q^{81} + 48q^{89} + 48q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(384, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
384.2.d.a \(2\) \(3.066\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+iq^{3}-4q^{7}-q^{9}+4iq^{11}+4iq^{13}+\cdots\)
384.2.d.b \(2\) \(3.066\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q+iq^{3}+4q^{7}-q^{9}+4iq^{11}-4iq^{13}+\cdots\)
384.2.d.c \(4\) \(3.066\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

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