Properties

Label 671.2.c
Level $671$
Weight $2$
Character orbit 671.c
Rep. character $\chi_{671}(243,\cdot)$
Character field $\Q$
Dimension $52$
Newform subspaces $1$
Sturm bound $124$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 671 = 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 671.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 61 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(124\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(671, [\chi])\).

Total New Old
Modular forms 64 52 12
Cusp forms 60 52 8
Eisenstein series 4 0 4

Trace form

\( 52 q + 4 q^{3} - 46 q^{4} + 44 q^{9} + O(q^{10}) \) \( 52 q + 4 q^{3} - 46 q^{4} + 44 q^{9} - 32 q^{12} - 24 q^{13} + 36 q^{14} + 8 q^{15} + 50 q^{16} - 36 q^{19} - 4 q^{20} - 2 q^{22} + 60 q^{25} + 16 q^{27} + 16 q^{34} - 42 q^{36} - 40 q^{39} + 16 q^{41} - 28 q^{42} - 52 q^{45} - 4 q^{46} - 36 q^{47} + 68 q^{48} - 36 q^{49} + 36 q^{52} - 104 q^{56} + 4 q^{57} - 56 q^{60} - 12 q^{61} + 52 q^{62} - 18 q^{64} - 44 q^{65} + 8 q^{66} + 44 q^{70} + 12 q^{73} - 40 q^{74} + 40 q^{75} + 64 q^{76} - 4 q^{77} + 28 q^{80} + 36 q^{81} + 28 q^{83} + 28 q^{86} - 18 q^{88} + 52 q^{95} + 20 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(671, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
671.2.c.a 671.c 61.b $52$ $5.358$ None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(671, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(671, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(61, [\chi])\)\(^{\oplus 2}\)