Properties

Label 980.2.c
Level $980$
Weight $2$
Character orbit 980.c
Rep. character $\chi_{980}(979,\cdot)$
Character field $\Q$
Dimension $112$
Newform subspaces $5$
Sturm bound $336$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(336\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 184 128 56
Cusp forms 152 112 40
Eisenstein series 32 16 16

Trace form

\( 112q + 4q^{4} - 88q^{9} + O(q^{10}) \) \( 112q + 4q^{4} - 88q^{9} - 4q^{16} + 12q^{25} - 24q^{29} - 28q^{30} + 36q^{36} + 4q^{44} + 4q^{46} - 4q^{50} - 96q^{60} - 44q^{64} + 40q^{65} - 76q^{74} + 24q^{81} + 52q^{85} + 24q^{86} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(980, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
980.2.c.a \(8\) \(7.825\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{2}q^{2}-2q^{4}-\zeta_{16}^{4}q^{5}+2\zeta_{16}^{2}q^{8}+\cdots\)
980.2.c.b \(8\) \(7.825\) 8.0.3317760000.3 \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+2q^{4}+\beta _{6}q^{5}+(-\beta _{5}+\cdots)q^{6}+\cdots\)
980.2.c.c \(16\) \(7.825\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(-\beta _{8}-\beta _{10}-\beta _{12})q^{3}+\cdots\)
980.2.c.d \(32\) \(7.825\) None \(0\) \(0\) \(0\) \(0\)
980.2.c.e \(48\) \(7.825\) None \(0\) \(0\) \(0\) \(0\)

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

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