Properties

Label 946.2.l
Level $946$
Weight $2$
Character orbit 946.l
Rep. character $\chi_{946}(85,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $176$
Newform subspaces $2$
Sturm bound $264$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 946 = 2 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 946.l (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 473 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(264\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(946, [\chi])\).

Total New Old
Modular forms 544 176 368
Cusp forms 512 176 336
Eisenstein series 32 0 32

Trace form

\( 176 q - 44 q^{4} + 10 q^{6} + 40 q^{9} + O(q^{10}) \) \( 176 q - 44 q^{4} + 10 q^{6} + 40 q^{9} - 14 q^{11} + 10 q^{13} - 16 q^{15} - 44 q^{16} - 20 q^{17} + 20 q^{23} - 10 q^{24} + 12 q^{25} - 8 q^{31} + 120 q^{35} + 50 q^{36} + 44 q^{38} + 26 q^{44} - 34 q^{47} + 24 q^{49} + 40 q^{52} - 10 q^{57} + 12 q^{58} + 30 q^{59} + 24 q^{60} - 44 q^{64} - 20 q^{66} + 24 q^{67} + 20 q^{68} - 40 q^{74} + 8 q^{78} - 40 q^{79} - 50 q^{81} + 10 q^{83} + 25 q^{86} - 100 q^{95} + 56 q^{97} + 184 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(946, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
946.2.l.a 946.l 473.k $88$ $7.554$ None \(-22\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
946.2.l.b 946.l 473.k $88$ $7.554$ None \(22\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(946, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(946, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(473, [\chi])\)\(^{\oplus 2}\)