Properties

Label 384.3.i
Level $384$
Weight $3$
Character orbit 384.i
Rep. character $\chi_{384}(161,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $56$
Newform subspaces $4$
Sturm bound $192$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 384.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(192\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(384, [\chi])\).

Total New Old
Modular forms 288 72 216
Cusp forms 224 56 168
Eisenstein series 64 16 48

Trace form

\( 56q + O(q^{10}) \) \( 56q + 8q^{13} - 32q^{21} - 8q^{33} + 8q^{37} + 104q^{45} - 72q^{49} + 72q^{61} + 40q^{69} - 8q^{81} + 128q^{85} + 136q^{93} - 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(384, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
384.3.i.a \(8\) \(10.463\) 8.0.629407744.1 None \(0\) \(-4\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(3\beta _{4}-\beta _{6}-\beta _{7})q^{5}+\cdots\)
384.3.i.b \(8\) \(10.463\) 8.0.629407744.1 None \(0\) \(4\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(3\beta _{4}-\beta _{6}+\cdots)q^{5}+\cdots\)
384.3.i.c \(20\) \(10.463\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-6\) \(0\) \(0\) \(q-\beta _{5}q^{3}+(\beta _{8}-\beta _{9}-\beta _{10})q^{5}-\beta _{6}q^{7}+\cdots\)
384.3.i.d \(20\) \(10.463\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(6\) \(0\) \(0\) \(q+\beta _{5}q^{3}+(\beta _{8}-\beta _{9}-\beta _{10})q^{5}+\beta _{6}q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

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