Properties

Label 800.2.bq
Level $800$
Weight $2$
Character orbit 800.bq
Rep. character $\chi_{800}(63,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $240$
Newform subspaces $4$
Sturm bound $240$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 800.bq (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 4 \)
Sturm bound: \(240\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(800, [\chi])\).

Total New Old
Modular forms 1024 240 784
Cusp forms 896 240 656
Eisenstein series 128 0 128

Trace form

\( 240 q + O(q^{10}) \) \( 240 q - 4 q^{13} + 12 q^{17} + 12 q^{25} + 16 q^{33} + 20 q^{37} + 20 q^{45} + 52 q^{53} - 32 q^{57} - 44 q^{65} - 28 q^{73} - 48 q^{77} + 60 q^{81} + 32 q^{85} - 60 q^{89} + 80 q^{93} - 204 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
800.2.bq.a 800.bq 100.l $56$ $6.388$ None \(0\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{20}]$
800.2.bq.b 800.bq 100.l $56$ $6.388$ None \(0\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{20}]$
800.2.bq.c 800.bq 100.l $64$ $6.388$ None \(0\) \(0\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{20}]$
800.2.bq.d 800.bq 100.l $64$ $6.388$ None \(0\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)