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Properties

Label 864.2.w
Level $864$
Weight $2$
Character orbit 864.w
Rep. character $\chi_{864}(107,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $256$
Newform subspaces $2$
Sturm bound $288$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.w (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(864, [\chi])\).

Total New Old
Modular forms 600 256 344
Cusp forms 552 256 296
Eisenstein series 48 0 48

Trace form

\( 256 q + O(q^{10}) \) \( 256 q - 8 q^{10} + 64 q^{16} - 16 q^{22} + 32 q^{40} + 32 q^{46} + 56 q^{52} + 32 q^{55} + 32 q^{58} - 32 q^{61} + 48 q^{64} - 128 q^{67} + 48 q^{70} - 64 q^{76} + 32 q^{79} - 40 q^{82} - 40 q^{88} + 48 q^{91} - 72 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(864, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
864.2.w.a 864.w 96.o $128$ $6.899$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
864.2.w.b 864.w 96.o $128$ $6.899$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)