Properties

Label 320.2.j
Level $320$
Weight $2$
Character orbit 320.j
Rep. character $\chi_{320}(47,\cdot)$
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.j (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

\( 20 q - 2 q^{5} + 4 q^{7} - 12 q^{9} + O(q^{10}) \) \( 20 q - 2 q^{5} + 4 q^{7} - 12 q^{9} + 4 q^{11} - 4 q^{13} - 12 q^{15} - 4 q^{17} - 8 q^{19} - 4 q^{21} + 4 q^{23} - 4 q^{33} - 4 q^{37} + 36 q^{43} - 6 q^{45} + 24 q^{47} - 4 q^{51} + 4 q^{55} + 12 q^{57} + 16 q^{59} + 12 q^{61} - 12 q^{63} - 4 q^{65} - 20 q^{67} + 28 q^{69} - 24 q^{71} + 8 q^{73} - 48 q^{75} - 20 q^{81} - 12 q^{85} - 52 q^{87} - 12 q^{91} + 8 q^{93} + 40 q^{95} - 4 q^{97} + 20 q^{99} + O(q^{100}) \)

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.j.a \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(6\) \(q-2iq^{3}+(1+2i)q^{5}+(3+3i)q^{7}+\cdots\)
320.2.j.b \(18\) \(2.555\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(-4\) \(-2\) \(q-\beta _{12}q^{3}-\beta _{4}q^{5}+\beta _{10}q^{7}+(-1+\cdots)q^{9}+\cdots\)

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

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