Properties

Label 384.2.f
Level $384$
Weight $2$
Character orbit 384.f
Rep. character $\chi_{384}(191,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $4$
Sturm bound $128$
Trace bound $15$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(128\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(5\), \(7\), \(23\)

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

\( 16q + O(q^{10}) \) \( 16q + 16q^{25} + 16q^{33} - 48q^{49} + 16q^{57} - 32q^{73} - 48q^{81} + O(q^{100}) \)

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.f.a \(4\) \(3.066\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}-3q^{9}-2\beta _{2}q^{11}+\cdots\)
384.2.f.b \(4\) \(3.066\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+(\zeta_{8}+\zeta_{8}^{2})q^{5}-\zeta_{8}^{3}q^{7}+\cdots\)
384.2.f.c \(4\) \(3.066\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+(1-\zeta_{8}^{2})q^{9}+(-2\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots\)
384.2.f.d \(4\) \(3.066\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+(-\zeta_{8}-\zeta_{8}^{2})q^{5}+\zeta_{8}^{3}q^{7}+\cdots\)

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

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