Properties

Label 861.2.bd
Level $861$
Weight $2$
Character orbit 861.bd
Rep. character $\chi_{861}(461,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $432$
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.bd (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 861 \)
Character field: \(\Q(\zeta_{10})\)
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 464 464 0
Cusp forms 432 432 0
Eisenstein series 32 32 0

Trace form

\( 432 q + 92 q^{4} - 6 q^{7} - 24 q^{9} + O(q^{10}) \) \( 432 q + 92 q^{4} - 6 q^{7} - 24 q^{9} - 36 q^{15} - 124 q^{16} + 6 q^{18} - 13 q^{21} - 16 q^{22} - 112 q^{25} + 10 q^{28} + 32 q^{30} + 66 q^{36} - 28 q^{37} - 8 q^{39} + 4 q^{42} - 4 q^{43} - 136 q^{46} - 50 q^{49} - 54 q^{51} + 48 q^{57} - 36 q^{58} - 118 q^{60} + 22 q^{63} + 28 q^{64} + 24 q^{67} - 46 q^{70} + 44 q^{72} + 54 q^{78} - 48 q^{79} + 88 q^{81} + 12 q^{84} + 24 q^{85} - 104 q^{88} - 92 q^{91} + 60 q^{93} + 40 q^{99} + O(q^{100}) \)

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.bd.a 861.bd 861.ad $432$ $6.875$ None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{10}]$