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Properties

Label 800.2.y
Level $800$
Weight $2$
Character orbit 800.y
Rep. character $\chi_{800}(101,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $292$
Newform subspaces $6$
Sturm bound $240$
Trace bound $18$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 800.y (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 6 \)
Sturm bound: \(240\)
Trace bound: \(18\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 504 316 188
Cusp forms 456 292 164
Eisenstein series 48 24 24

Trace form

\( 292 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 12 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} + O(q^{10}) \) \( 292 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 12 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} - 12 q^{11} - 12 q^{12} + 4 q^{13} - 12 q^{14} + 8 q^{16} + 24 q^{18} + 4 q^{19} - 12 q^{21} - 16 q^{22} + 12 q^{23} - 24 q^{24} + 8 q^{26} + 28 q^{27} - 16 q^{28} + 4 q^{29} - 48 q^{31} - 16 q^{32} + 8 q^{33} + 8 q^{34} + 40 q^{36} + 4 q^{37} - 44 q^{38} + 28 q^{39} - 12 q^{41} + 24 q^{42} + 12 q^{43} + 44 q^{44} + 20 q^{46} - 48 q^{48} - 8 q^{51} + 12 q^{52} + 20 q^{53} + 80 q^{54} - 24 q^{56} + 4 q^{57} - 64 q^{58} + 36 q^{59} - 44 q^{61} - 32 q^{63} + 40 q^{64} + 12 q^{66} - 36 q^{67} - 64 q^{68} - 28 q^{69} + 20 q^{71} - 92 q^{72} + 4 q^{73} - 92 q^{74} - 12 q^{76} + 20 q^{77} - 108 q^{78} + 4 q^{82} + 44 q^{83} - 16 q^{84} - 96 q^{86} - 52 q^{87} - 80 q^{88} + 4 q^{89} + 36 q^{91} + 48 q^{92} + 16 q^{93} - 88 q^{94} - 152 q^{96} + 8 q^{97} - 56 q^{98} - 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.y.a 800.y 32.g $4$ $6.388$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+\cdots\)
800.2.y.b 800.y 32.g $8$ $6.388$ 8.0.18939904.2 None \(4\) \(4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{8}]$ \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{3}-\beta _{5}-\beta _{7})q^{3}+\cdots\)
800.2.y.c 800.y 32.g $64$ $6.388$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
800.2.y.d 800.y 32.g $64$ $6.388$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
800.2.y.e 800.y 32.g $64$ $6.388$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
800.2.y.f 800.y 32.g $88$ $6.388$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

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

\( S_{2}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)