Properties

Label 980.1.p
Level $980$
Weight $1$
Character orbit 980.p
Rep. character $\chi_{980}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $3$
Sturm bound $168$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 980.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(168\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(980, [\chi])\).

Total New Old
Modular forms 52 28 24
Cusp forms 20 12 8
Eisenstein series 32 16 16

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12q + 2q^{4} + 2q^{5} + 4q^{6} + 4q^{9} + O(q^{10}) \) \( 12q + 2q^{4} + 2q^{5} + 4q^{6} + 4q^{9} - 6q^{16} - 4q^{20} - 2q^{24} - 2q^{25} - 4q^{29} + 2q^{30} + 8q^{36} + 4q^{41} + 2q^{46} - 8q^{50} + 2q^{54} - 2q^{61} - 4q^{64} + 4q^{65} - 4q^{69} - 8q^{74} + 2q^{80} - 2q^{81} - 8q^{85} + 2q^{86} - 2q^{89} + 4q^{94} - 2q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(980, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
980.1.p.a \(2\) \(0.489\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-5}) \) None \(-1\) \(-1\) \(1\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\)
980.1.p.b \(2\) \(0.489\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-5}) \) None \(1\) \(1\) \(1\) \(0\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\)
980.1.p.c \(8\) \(0.489\) \(\Q(\zeta_{24})\) \(D_{4}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}-\zeta_{24}^{7}q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(980, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(980, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)