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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
980.2.c.a 980.c 140.c $8$ $7.825$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-1}) \) 980.2.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta_{2} q^{2}-2 q^{4}-\beta_{4} q^{5}+2\beta_{2} q^{8}+\cdots\)
980.2.c.b 980.c 140.c $8$ $7.825$ 8.0.3317760000.3 \(\Q(\sqrt{-5}) \) 140.2.s.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+2q^{4}+\beta _{6}q^{5}+(-\beta _{5}+\cdots)q^{6}+\cdots\)
980.2.c.c 980.c 140.c $16$ $7.825$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 980.2.c.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(-\beta _{8}-\beta _{10}-\beta _{12})q^{3}+\cdots\)
980.2.c.d 980.c 140.c $32$ $7.825$ None 140.2.s.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
980.2.c.e 980.c 140.c $48$ $7.825$ None 980.2.c.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

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