Properties

Label 768.2.o
Level 768
Weight 2
Character orbit o
Rep. character \(\chi_{768}(95,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 112
Newform subspaces 2
Sturm bound 256
Trace bound 3

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.o (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(256\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 576 144 432
Cusp forms 448 112 336
Eisenstein series 128 32 96

Trace form

\( 112q - 8q^{9} + O(q^{10}) \) \( 112q - 8q^{9} + 16q^{13} + 8q^{21} - 16q^{25} - 16q^{33} + 16q^{37} + 8q^{45} - 8q^{57} + 80q^{61} + 8q^{69} - 16q^{73} + 96q^{85} - 16q^{93} - 32q^{97} + O(q^{100}) \)

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.o.a \(56\) \(6.133\) None \(0\) \(-4\) \(0\) \(8\)
768.2.o.b \(56\) \(6.133\) None \(0\) \(4\) \(0\) \(-8\)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database