Properties

Label 768.2.n
Level $768$
Weight $2$
Character orbit 768.n
Rep. character $\chi_{768}(97,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $64$
Newform subspaces $2$
Sturm bound $256$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.n (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(256\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(768, [\chi])\).

Total New Old
Modular forms 576 64 512
Cusp forms 448 64 384
Eisenstein series 128 0 128

Trace form

\( 64q + O(q^{10}) \) \( 64q + 64q^{53} + 64q^{61} + 64q^{69} + 64q^{77} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(768, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
768.2.n.a \(32\) \(6.133\) None \(0\) \(0\) \(0\) \(0\)
768.2.n.b \(32\) \(6.133\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(768, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(768, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)