Properties

Label 320.2.n
Level $320$
Weight $2$
Character orbit 320.n
Rep. character $\chi_{320}(63,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
Newform subspaces $9$
Sturm bound $96$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 9 \)
Sturm bound: \(96\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\), \(13\)

Dimensions

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

Total New Old
Modular forms 120 28 92
Cusp forms 72 20 52
Eisenstein series 48 8 40

Trace form

\( 20q + 4q^{5} + O(q^{10}) \) \( 20q + 4q^{5} + 4q^{13} - 12q^{17} + 8q^{21} - 12q^{25} + 8q^{33} + 4q^{37} - 8q^{41} - 16q^{45} + 52q^{53} - 16q^{57} - 24q^{61} + 4q^{65} - 12q^{73} - 72q^{77} + 36q^{81} - 44q^{85} - 56q^{93} - 28q^{97} + O(q^{100}) \)

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.n.a \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(4\) \(4\) \(q+(-2-2i)q^{3}+(2-i)q^{5}+(2-2i)q^{7}+\cdots\)
320.2.n.b \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-2\) \(-6\) \(q+(-1-i)q^{3}+(-1-2i)q^{5}+(-3+\cdots)q^{7}+\cdots\)
320.2.n.c \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-2\) \(2\) \(q+(-1-i)q^{3}+(-1+2i)q^{5}+(1-i)q^{7}+\cdots\)
320.2.n.d \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-4\) \(0\) \(q+(-2-i)q^{5}-3iq^{9}+(5-5i)q^{13}+\cdots\)
320.2.n.e \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(4\) \(0\) \(q+(2-i)q^{5}-3iq^{9}+(1-i)q^{13}+(3+\cdots)q^{17}+\cdots\)
320.2.n.f \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-2\) \(-2\) \(q+(1+i)q^{3}+(-1+2i)q^{5}+(-1+i)q^{7}+\cdots\)
320.2.n.g \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-2\) \(6\) \(q+(1+i)q^{3}+(-1-2i)q^{5}+(3-3i)q^{7}+\cdots\)
320.2.n.h \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(4\) \(-4\) \(q+(2+2i)q^{3}+(2-i)q^{5}+(-2+2i)q^{7}+\cdots\)
320.2.n.i \(4\) \(2.555\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{12}^{2}q^{3}+(1+2\zeta_{12})q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)