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Properties

Label 980.2.i
Level $980$
Weight $2$
Character orbit 980.i
Rep. character $\chi_{980}(361,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $28$
Newform subspaces $12$
Sturm bound $336$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
Sturm bound: \(336\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

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

Total New Old
Modular forms 384 28 356
Cusp forms 288 28 260
Eisenstein series 96 0 96

Trace form

\( 28 q - 2 q^{3} - 2 q^{5} - 10 q^{9} + O(q^{10}) \) \( 28 q - 2 q^{3} - 2 q^{5} - 10 q^{9} + 6 q^{11} + 8 q^{13} - 8 q^{15} - 4 q^{17} + 8 q^{19} - 6 q^{23} - 14 q^{25} + 28 q^{27} - 16 q^{29} + 4 q^{31} + 12 q^{33} - 12 q^{37} - 10 q^{39} - 4 q^{41} + 60 q^{43} - 4 q^{45} + 8 q^{47} - 14 q^{51} + 24 q^{53} + 8 q^{55} + 24 q^{57} - 8 q^{59} + 6 q^{61} + 6 q^{65} - 46 q^{67} - 60 q^{69} - 16 q^{71} + 4 q^{73} - 2 q^{75} - 26 q^{79} - 6 q^{81} - 4 q^{83} - 20 q^{85} - 6 q^{87} + 10 q^{89} - 40 q^{93} - 12 q^{95} + 40 q^{97} - 120 q^{99} + O(q^{100}) \)

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.i.a 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots\)
980.2.i.b 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots\)
980.2.i.c 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
980.2.i.d 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
980.2.i.e 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
980.2.i.f 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots\)
980.2.i.g 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots\)
980.2.i.h 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots\)
980.2.i.i 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+2q^{13}+\cdots\)
980.2.i.j 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+(5+\cdots)q^{11}+\cdots\)
980.2.i.k 980.i 7.c $4$ $7.825$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{3}-\beta _{2}q^{5}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
980.2.i.l 980.i 7.c $4$ $7.825$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(2\beta _{1}+2\beta _{3})q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(980, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)