Properties

Label 320.2.s
Level $320$
Weight $2$
Character orbit 320.s
Rep. character $\chi_{320}(207,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(320, [\chi])\).

Total New Old
Modular forms 112 28 84
Cusp forms 80 20 60
Eisenstein series 32 8 24

Trace form

\( 20q + 4q^{3} - 2q^{5} + 4q^{7} + 12q^{9} + O(q^{10}) \) \( 20q + 4q^{3} - 2q^{5} + 4q^{7} + 12q^{9} + 4q^{11} + 12q^{15} - 4q^{17} + 8q^{19} - 4q^{21} + 4q^{23} + 16q^{27} - 4q^{33} - 20q^{35} - 18q^{45} - 24q^{47} - 4q^{51} - 4q^{53} + 4q^{55} - 12q^{57} - 16q^{59} + 12q^{61} + 12q^{63} - 4q^{65} - 28q^{69} - 24q^{71} - 8q^{73} - 4q^{75} - 32q^{77} - 20q^{81} - 36q^{83} + 8q^{85} - 52q^{87} - 12q^{91} - 40q^{95} - 4q^{97} - 20q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
320.2.s.a \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(-4\) \(6\) \(q+2q^{3}+(-2+i)q^{5}+(3+3i)q^{7}+\cdots\)
320.2.s.b \(18\) \(2.555\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(2\) \(-2\) \(q-\beta _{1}q^{3}+\beta _{7}q^{5}+\beta _{10}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)