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Properties

Label 980.2.bk
Level $980$
Weight $2$
Character orbit 980.bk
Rep. character $\chi_{980}(43,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $1968$
Newform subspaces $1$
Sturm bound $336$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.bk (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 980 \)
Character field: \(\Q(\zeta_{28})\)
Newform subspaces: \( 1 \)
Sturm bound: \(336\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(980, [\chi])\).

Total New Old
Modular forms 2064 2064 0
Cusp forms 1968 1968 0
Eisenstein series 96 96 0

Trace form

\( 1968 q - 10 q^{2} - 20 q^{5} - 20 q^{6} - 22 q^{8} + O(q^{10}) \) \( 1968 q - 10 q^{2} - 20 q^{5} - 20 q^{6} - 22 q^{8} - 10 q^{10} + 2 q^{12} - 20 q^{13} - 4 q^{16} - 20 q^{17} - 44 q^{18} - 26 q^{20} - 56 q^{21} - 18 q^{22} - 20 q^{25} - 4 q^{26} - 14 q^{28} - 4 q^{30} - 10 q^{32} - 28 q^{33} - 52 q^{36} - 20 q^{37} - 42 q^{38} + 30 q^{40} - 24 q^{41} + 6 q^{42} - 60 q^{45} - 20 q^{46} - 4 q^{48} + 192 q^{50} - 22 q^{52} - 20 q^{53} - 4 q^{56} - 80 q^{57} - 50 q^{58} - 34 q^{60} - 40 q^{61} - 26 q^{62} - 20 q^{65} - 256 q^{66} - 84 q^{68} - 154 q^{70} + 120 q^{72} - 36 q^{73} - 148 q^{76} - 28 q^{77} + 86 q^{78} - 40 q^{80} + 24 q^{81} + 38 q^{82} + 28 q^{85} - 108 q^{86} - 152 q^{88} - 10 q^{90} + 42 q^{92} + 40 q^{93} + 104 q^{96} - 128 q^{97} - 280 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(980, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
980.2.bk.a 980.bk 980.ak $1968$ $7.825$ None \(-10\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{28}]$