Properties

Label 384.2.c
Level $384$
Weight $2$
Character orbit 384.c
Rep. character $\chi_{384}(383,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $4$
Sturm bound $128$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(128\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(11\), \(23\)

Dimensions

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

Total New Old
Modular forms 80 16 64
Cusp forms 48 16 32
Eisenstein series 32 0 32

Trace form

\( 16q + O(q^{10}) \) \( 16q - 16q^{25} + 16q^{33} + 16q^{49} - 16q^{57} - 32q^{73} + 16q^{81} - 64q^{97} + O(q^{100}) \)

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.c.a \(4\) \(3.066\) \(\Q(i, \sqrt{5})\) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1+\beta _{3})q^{3}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
384.2.c.b \(4\) \(3.066\) \(\Q(i, \sqrt{5})\) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1+\beta _{3})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
384.2.c.c \(4\) \(3.066\) \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
384.2.c.d \(4\) \(3.066\) \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)