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Properties

Label 980.2.bu
Level $980$
Weight $2$
Character orbit 980.bu
Rep. character $\chi_{980}(17,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $672$
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.bu (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{84})\)
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 4176 672 3504
Cusp forms 3888 672 3216
Eisenstein series 288 0 288

Trace form

\( 672 q - 6 q^{5} - 2 q^{7} + O(q^{10}) \) \( 672 q - 6 q^{5} - 2 q^{7} + 4 q^{11} - 8 q^{15} - 4 q^{17} + 4 q^{21} + 4 q^{23} + 2 q^{25} + 12 q^{31} + 42 q^{33} + 40 q^{35} + 6 q^{37} + 56 q^{41} - 36 q^{43} - 46 q^{45} - 36 q^{47} + 104 q^{51} - 80 q^{53} + 42 q^{55} - 2 q^{57} + 52 q^{61} - 48 q^{63} - 18 q^{65} - 16 q^{67} + 8 q^{71} - 78 q^{73} - 12 q^{75} - 10 q^{77} - 36 q^{81} - 14 q^{83} + 32 q^{85} - 2 q^{87} - 76 q^{91} - 200 q^{93} + 14 q^{95} + O(q^{100}) \)

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.bu.a 980.bu 245.x $672$ $7.825$ None \(0\) \(0\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{84}]$

Decomposition of \(S_{2}^{\mathrm{old}}(980, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(980, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)