Properties

Label 861.2.bz
Level $861$
Weight $2$
Character orbit 861.bz
Rep. character $\chi_{861}(4,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $448$
Newform subspaces $1$
Sturm bound $224$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 861 = 3 \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 861.bz (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(861, [\chi])\).

Total New Old
Modular forms 928 448 480
Cusp forms 864 448 416
Eisenstein series 64 0 64

Trace form

\( 448 q + 56 q^{4} - 24 q^{8} + 224 q^{9} + O(q^{10}) \) \( 448 q + 56 q^{4} - 24 q^{8} + 224 q^{9} - 10 q^{10} + 56 q^{16} + 72 q^{20} - 40 q^{22} + 12 q^{23} + 40 q^{25} - 50 q^{28} + 40 q^{29} + 16 q^{31} + 4 q^{32} - 8 q^{33} - 120 q^{34} - 20 q^{35} + 112 q^{36} + 22 q^{37} - 52 q^{40} + 52 q^{41} - 8 q^{42} + 8 q^{43} - 12 q^{46} - 60 q^{47} - 56 q^{49} - 88 q^{50} - 20 q^{51} + 100 q^{52} - 120 q^{56} + 24 q^{57} + 20 q^{59} - 48 q^{61} + 36 q^{62} - 40 q^{64} - 90 q^{65} + 40 q^{66} - 20 q^{67} - 40 q^{69} + 10 q^{70} + 40 q^{71} - 12 q^{72} + 52 q^{73} - 4 q^{74} + 40 q^{75} - 60 q^{76} - 76 q^{77} - 172 q^{80} - 224 q^{81} + 88 q^{82} - 136 q^{83} - 72 q^{84} + 44 q^{86} - 24 q^{87} - 230 q^{88} + 60 q^{89} - 20 q^{90} - 124 q^{91} - 44 q^{92} + 60 q^{93} + 150 q^{94} - 40 q^{97} - 148 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(861, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
861.2.bz.a 861.bz 287.z $448$ $6.875$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{30}]$

Decomposition of \(S_{2}^{\mathrm{old}}(861, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(861, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 2}\)