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Properties

Label 1980.2.q
Level $1980$
Weight $2$
Character orbit 1980.q
Rep. character $\chi_{1980}(661,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $8$
Sturm bound $864$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1980.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 8 \)
Sturm bound: \(864\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1980, [\chi])\).

Total New Old
Modular forms 888 80 808
Cusp forms 840 80 760
Eisenstein series 48 0 48

Trace form

\( 80 q - 4 q^{5} + 4 q^{7} - 4 q^{9} + O(q^{10}) \) \( 80 q - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{13} - 8 q^{19} - 8 q^{21} - 40 q^{25} + 4 q^{29} - 8 q^{31} - 8 q^{37} - 16 q^{39} - 4 q^{41} - 8 q^{43} + 16 q^{45} + 24 q^{47} - 24 q^{49} + 80 q^{53} + 16 q^{57} + 16 q^{59} + 40 q^{61} + 64 q^{63} + 28 q^{67} - 36 q^{69} - 64 q^{71} - 56 q^{73} - 16 q^{77} + 4 q^{79} - 28 q^{81} - 16 q^{83} - 8 q^{87} - 56 q^{89} - 40 q^{91} - 32 q^{93} - 8 q^{95} + 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1980, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1980.2.q.a 1980.q 9.c $2$ $15.810$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(-1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots\)
1980.2.q.b 1980.q 9.c $2$ $15.810$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{5}-3q^{9}+(-1+\cdots)q^{11}+\cdots\)
1980.2.q.c 1980.q 9.c $2$ $15.810$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots\)
1980.2.q.d 1980.q 9.c $4$ $15.810$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(0\) \(0\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\beta _{1})q^{3}+(1-\beta _{1})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1980.2.q.e 1980.q 9.c $14$ $15.810$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(7\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{3}+\beta _{4})q^{3}+(1-\beta _{3})q^{5}+(\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
1980.2.q.f 1980.q 9.c $16$ $15.810$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(8\) \(7\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+(1-\beta _{3})q^{5}+(\beta _{3}-\beta _{11}-\beta _{14}+\cdots)q^{7}+\cdots\)
1980.2.q.g 1980.q 9.c $18$ $15.810$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(3\) \(-9\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{6}q^{3}+(-1-\beta _{2})q^{5}+(\beta _{2}-\beta _{10}+\cdots)q^{7}+\cdots\)
1980.2.q.h 1980.q 9.c $22$ $15.810$ None \(0\) \(0\) \(-11\) \(5\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1980, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1980, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(990, [\chi])\)\(^{\oplus 2}\)