Properties

Label 980.2.e
Level $980$
Weight $2$
Character orbit 980.e
Rep. character $\chi_{980}(589,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $6$
Sturm bound $336$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(336\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(11\), \(19\)

Dimensions

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

Total New Old
Modular forms 192 20 172
Cusp forms 144 20 124
Eisenstein series 48 0 48

Trace form

\( 20 q + 2 q^{5} - 20 q^{9} + O(q^{10}) \) \( 20 q + 2 q^{5} - 20 q^{9} - 4 q^{11} + 10 q^{15} - 8 q^{19} - 6 q^{25} + 4 q^{29} + 20 q^{31} - 30 q^{45} + 28 q^{51} + 12 q^{55} - 28 q^{59} + 12 q^{61} - 36 q^{65} + 12 q^{69} - 40 q^{71} - 24 q^{75} - 20 q^{79} + 4 q^{81} + 10 q^{85} - 4 q^{89} + 34 q^{95} + 48 q^{99} + O(q^{100}) \)

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.e.a 980.e 5.b $2$ $7.825$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-i)q^{5}+3q^{9}+2iq^{13}-2iq^{17}+\cdots\)
980.2.e.b 980.e 5.b $2$ $7.825$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+(2+i)q^{5}-6q^{9}+3q^{11}+\cdots\)
980.2.e.c 980.e 5.b $4$ $7.825$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-2-\beta _{1}-\beta _{3})q^{11}+\cdots\)
980.2.e.d 980.e 5.b $4$ $7.825$ \(\Q(\sqrt{-5}, \sqrt{-21})\) \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-4+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots\)
980.2.e.e 980.e 5.b $4$ $7.825$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}-q^{11}-\beta _{2}q^{13}+\cdots\)
980.2.e.f 980.e 5.b $4$ $7.825$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}-\beta _{3}q^{5}+(-2-\beta _{1}-\beta _{3})q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(980, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)