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Properties

Label 806.2.cc
Level $806$
Weight $2$
Character orbit 806.cc
Rep. character $\chi_{806}(21,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $576$
Newform subspaces $1$
Sturm bound $224$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 806 = 2 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 806.cc (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 403 \)
Character field: \(\Q(\zeta_{60})\)
Newform subspaces: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(806, [\chi])\).

Total New Old
Modular forms 1856 576 1280
Cusp forms 1728 576 1152
Eisenstein series 128 0 128

Trace form

\( 576 q + 4 q^{7} - 64 q^{9} + O(q^{10}) \) \( 576 q + 4 q^{7} - 64 q^{9} + 8 q^{11} + 20 q^{13} - 24 q^{14} + 144 q^{16} - 16 q^{18} - 8 q^{21} + 12 q^{22} + 48 q^{26} + 60 q^{27} - 36 q^{28} + 36 q^{31} - 52 q^{33} - 56 q^{34} - 8 q^{35} + 60 q^{37} - 8 q^{39} - 40 q^{41} - 36 q^{42} - 12 q^{44} - 36 q^{45} - 40 q^{46} + 8 q^{47} + 52 q^{53} + 144 q^{57} - 4 q^{59} - 328 q^{63} - 76 q^{65} - 32 q^{66} - 48 q^{70} - 20 q^{71} + 16 q^{72} - 48 q^{73} + 48 q^{74} + 60 q^{76} + 40 q^{78} + 16 q^{79} + 216 q^{81} - 284 q^{83} + 32 q^{84} - 80 q^{85} + 156 q^{86} - 32 q^{87} - 220 q^{89} - 60 q^{91} + 44 q^{93} - 16 q^{94} + 248 q^{97} - 72 q^{98} + 240 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(806, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
806.2.cc.a 806.cc 403.bd $576$ $6.436$ None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{60}]$

Decomposition of \(S_{2}^{\mathrm{old}}(806, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(806, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(403, [\chi])\)\(^{\oplus 2}\)