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Properties

Label 980.2.bg
Level $980$
Weight $2$
Character orbit 980.bg
Rep. character $\chi_{980}(81,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $216$
Newform subspaces $3$
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.bg (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 3 \)
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 2088 216 1872
Cusp forms 1944 216 1728
Eisenstein series 144 0 144

Trace form

\( 216 q - 2 q^{3} - 2 q^{5} - 6 q^{7} + 32 q^{9} + O(q^{10}) \) \( 216 q - 2 q^{3} - 2 q^{5} - 6 q^{7} + 32 q^{9} + 2 q^{11} + 8 q^{13} - 4 q^{17} + 8 q^{19} - 14 q^{21} - 48 q^{23} + 18 q^{25} - 14 q^{27} + 6 q^{29} + 4 q^{31} + 12 q^{33} + 14 q^{35} + 30 q^{37} + 8 q^{39} + 24 q^{41} - 28 q^{43} - 4 q^{45} + 148 q^{47} + 58 q^{49} + 46 q^{51} + 64 q^{53} + 8 q^{55} + 34 q^{59} - 36 q^{61} - 18 q^{63} + 2 q^{65} - 2 q^{67} - 4 q^{69} - 16 q^{71} - 38 q^{73} - 2 q^{75} - 46 q^{77} - 2 q^{79} - 72 q^{81} - 46 q^{83} + 4 q^{85} - 230 q^{87} - 144 q^{89} - 46 q^{91} + 4 q^{93} - 4 q^{95} - 72 q^{97} - 120 q^{99} + O(q^{100}) \)

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.bg.a 980.bg 49.g $12$ $7.825$ \(\Q(\zeta_{21})\) None \(0\) \(10\) \(1\) \(-14\) $\mathrm{SU}(2)[C_{21}]$ \(q+(1-\zeta_{21}+\zeta_{21}^{2}-\zeta_{21}^{3}-\zeta_{21}^{4}+\cdots)q^{3}+\cdots\)
980.2.bg.b 980.bg 49.g $84$ $7.825$ None \(0\) \(-11\) \(7\) \(14\) $\mathrm{SU}(2)[C_{21}]$
980.2.bg.c 980.bg 49.g $120$ $7.825$ None \(0\) \(-1\) \(-10\) \(-6\) $\mathrm{SU}(2)[C_{21}]$

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

\( S_{2}^{\mathrm{old}}(980, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)