Properties

Label 384.2.k
Level $384$
Weight $2$
Character orbit 384.k
Rep. character $\chi_{384}(95,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
Newform subspaces $2$
Sturm bound $128$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(128\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 160 40 120
Cusp forms 96 24 72
Eisenstein series 64 16 48

Trace form

\( 24q + O(q^{10}) \) \( 24q + 8q^{13} + 16q^{21} - 8q^{33} + 8q^{37} + 24q^{45} - 40q^{49} - 24q^{61} - 8q^{69} - 8q^{81} - 64q^{85} - 56q^{93} - 16q^{97} + O(q^{100}) \)

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.k.a \(12\) \(3.066\) 12.0.\(\cdots\).2 None \(0\) \(-2\) \(0\) \(8\) \(q+\beta _{4}q^{3}+\beta _{6}q^{5}+(1-\beta _{11})q^{7}+(-\beta _{3}+\cdots)q^{9}+\cdots\)
384.2.k.b \(12\) \(3.066\) 12.0.\(\cdots\).2 None \(0\) \(2\) \(0\) \(-8\) \(q-\beta _{10}q^{3}-\beta _{7}q^{5}+(-1+\beta _{11})q^{7}+\cdots\)

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

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