Properties

Label 768.1.e
Level $768$
Weight $1$
Character orbit 768.e
Rep. character $\chi_{768}(257,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $3$
Sturm bound $128$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 768.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(128\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(768, [\chi])\).

Total New Old
Modular forms 28 8 20
Cusp forms 4 4 0
Eisenstein series 24 4 20

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4q + O(q^{10}) \) \( 4q + 4q^{25} - 4q^{33} - 4q^{49} - 4q^{57} + 4q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(768, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
768.1.e.a \(1\) \(0.383\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{6}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{9}+2q^{19}+q^{25}-q^{27}+\cdots\)
768.1.e.b \(1\) \(0.383\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{6}) \) \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{9}-2q^{19}+q^{25}+q^{27}+\cdots\)
768.1.e.c \(2\) \(0.383\) \(\Q(\sqrt{-1}) \) \(D_{2}\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-q^{9}-iq^{11}+q^{25}+iq^{27}+\cdots\)