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Properties

Label 980.2.bi
Level $980$
Weight $2$
Character orbit 980.bi
Rep. character $\chi_{980}(13,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $336$
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.bi (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
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 2088 336 1752
Cusp forms 1944 336 1608
Eisenstein series 144 0 144

Trace form

\( 336 q + 2 q^{7} + O(q^{10}) \) \( 336 q + 2 q^{7} + 8 q^{11} + 8 q^{15} - 14 q^{17} + 8 q^{21} + 8 q^{23} + 4 q^{25} + 14 q^{35} + 12 q^{37} + 28 q^{41} + 36 q^{43} + 112 q^{45} + 42 q^{47} + 40 q^{51} + 50 q^{53} - 42 q^{55} + 2 q^{57} + 56 q^{61} - 42 q^{63} - 36 q^{65} - 32 q^{67} - 8 q^{71} - 84 q^{75} - 44 q^{77} + 12 q^{81} - 154 q^{83} - 32 q^{85} - 28 q^{87} + 148 q^{91} - 190 q^{93} + 28 q^{95} + O(q^{100}) \)

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.bi.a 980.bi 245.s $336$ $7.825$ None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{28}]$

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

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