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Properties

Label 980.2.g
Level $980$
Weight $2$
Character orbit 980.g
Rep. character $\chi_{980}(391,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $2$
Sturm bound $336$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(336\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 184 80 104
Cusp forms 152 80 72
Eisenstein series 32 0 32

Trace form

\( 80 q + 4 q^{2} - 4 q^{4} + 4 q^{8} + 80 q^{9} + O(q^{10}) \) \( 80 q + 4 q^{2} - 4 q^{4} + 4 q^{8} + 80 q^{9} - 12 q^{16} + 40 q^{18} - 40 q^{22} - 80 q^{25} + 24 q^{29} + 4 q^{32} + 20 q^{36} + 48 q^{37} + 36 q^{44} - 36 q^{46} - 4 q^{50} - 48 q^{53} + 48 q^{57} - 52 q^{58} - 28 q^{60} - 4 q^{64} - 8 q^{65} - 80 q^{72} + 20 q^{74} + 8 q^{78} + 120 q^{81} - 56 q^{86} + 24 q^{88} - 116 q^{92} + 16 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
980.2.g.a 980.g 28.d $32$ $7.825$ None 140.2.o.a \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
980.2.g.b 980.g 28.d $48$ $7.825$ None 980.2.g.b \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(980, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)