Properties

Label 1280.2.n
Level $1280$
Weight $2$
Character orbit 1280.n
Rep. character $\chi_{1280}(767,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $19$
Sturm bound $384$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1280 = 2^{8} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1280.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 19 \)
Sturm bound: \(384\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1280, [\chi])\).

Total New Old
Modular forms 432 104 328
Cusp forms 336 88 248
Eisenstein series 96 16 80

Trace form

\( 88q + O(q^{10}) \) \( 88q - 8q^{17} + 8q^{25} - 32q^{33} + 16q^{41} - 16q^{57} - 8q^{65} + 40q^{73} - 40q^{81} - 8q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1280, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1280.2.n.a \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(-2\) \(-4\) \(q+(-2-2i)q^{3}+(-1-2i)q^{5}+(-2+\cdots)q^{7}+\cdots\)
1280.2.n.b \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(2\) \(4\) \(q+(-2-2i)q^{3}+(1+2i)q^{5}+(2-2i)q^{7}+\cdots\)
1280.2.n.c \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(2\) \(q+(-1-i)q^{3}+(-2+i)q^{5}+(1-i)q^{7}+\cdots\)
1280.2.n.d \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(4\) \(-2\) \(q+(-1-i)q^{3}+(2-i)q^{5}+(-1+i)q^{7}+\cdots\)
1280.2.n.e \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) \(q+(-1-2i)q^{5}-3iq^{9}+(-5+5i)q^{13}+\cdots\)
1280.2.n.f \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) \(q+(-1+2i)q^{5}-3iq^{9}+(-1+i)q^{13}+\cdots\)
1280.2.n.g \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) \(q+(1-2i)q^{5}-3iq^{9}+(1-i)q^{13}+\cdots\)
1280.2.n.h \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) \(q+(1+2i)q^{5}-3iq^{9}+(5-5i)q^{13}+\cdots\)
1280.2.n.i \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-4\) \(-2\) \(q+(1+i)q^{3}+(-2+i)q^{5}+(-1+i)q^{7}+\cdots\)
1280.2.n.j \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(2\) \(q+(1+i)q^{3}+(2-i)q^{5}+(1-i)q^{7}+\cdots\)
1280.2.n.k \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(-2\) \(4\) \(q+(2+2i)q^{3}+(-1-2i)q^{5}+(2-2i)q^{7}+\cdots\)
1280.2.n.l \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(2\) \(-4\) \(q+(2+2i)q^{3}+(1+2i)q^{5}+(-2+2i)q^{7}+\cdots\)
1280.2.n.m \(8\) \(10.221\) \(\Q(\zeta_{20})\) None \(0\) \(-4\) \(0\) \(0\) \(q+(-1+\zeta_{20}^{2})q^{3}+(-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{5}+\cdots\)
1280.2.n.n \(8\) \(10.221\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(-4\) \(q+(-\beta _{2}-\beta _{7})q^{3}+(\beta _{2}+\beta _{4}+\beta _{7})q^{5}+\cdots\)
1280.2.n.o \(8\) \(10.221\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{3}-\beta _{4}q^{5}-\beta _{2}q^{7}-\beta _{3}q^{9}+\cdots\)
1280.2.n.p \(8\) \(10.221\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(4\) \(q+(-\beta _{2}-\beta _{7})q^{3}+(-\beta _{2}-\beta _{4}-\beta _{7})q^{5}+\cdots\)
1280.2.n.q \(8\) \(10.221\) \(\Q(\zeta_{20})\) None \(0\) \(4\) \(0\) \(0\) \(q+(1-\zeta_{20}^{2})q^{3}+(\zeta_{20}^{4}-\zeta_{20}^{6})q^{5}+\cdots\)
1280.2.n.r \(12\) \(10.221\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{2}q^{3}+\beta _{7}q^{5}+\beta _{6}q^{7}+(\beta _{5}+\beta _{7}+\cdots)q^{9}+\cdots\)
1280.2.n.s \(12\) \(10.221\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{2}q^{3}-\beta _{7}q^{5}-\beta _{6}q^{7}+(\beta _{5}+\beta _{7}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1280, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)