Properties

Label 1280.2.f
Level $1280$
Weight $2$
Character orbit 1280.f
Rep. character $\chi_{1280}(129,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $12$
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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(384\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(13\)

Dimensions

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

Total New Old
Modular forms 216 52 164
Cusp forms 168 44 124
Eisenstein series 48 8 40

Trace form

\( 44q + 44q^{9} + O(q^{10}) \) \( 44q + 44q^{9} + 4q^{25} + 8q^{41} - 28q^{49} + 28q^{81} - 24q^{89} + O(q^{100}) \)

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.f.a \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(-4\) \(0\) \(q-2q^{3}+(-2-i)q^{5}-2iq^{7}+q^{9}+\cdots\)
1280.2.f.b \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(4\) \(0\) \(q-2q^{3}+(2-i)q^{5}-2iq^{7}+q^{9}+4iq^{11}+\cdots\)
1280.2.f.c \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-4\) \(0\) \(q+(-2+i)q^{5}-3q^{9}+4q^{13}-8iq^{17}+\cdots\)
1280.2.f.d \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(4\) \(0\) \(q+(2+i)q^{5}-3q^{9}-4q^{13}+8iq^{17}+\cdots\)
1280.2.f.e \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(-4\) \(0\) \(q+2q^{3}+(-2-i)q^{5}+2iq^{7}+q^{9}+\cdots\)
1280.2.f.f \(2\) \(10.221\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(4\) \(0\) \(q+2q^{3}+(2-i)q^{5}+2iq^{7}+q^{9}-4iq^{11}+\cdots\)
1280.2.f.g \(4\) \(10.221\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\beta _{3})q^{3}-\beta _{2}q^{5}+(3\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1280.2.f.h \(4\) \(10.221\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) \(0\) \(4\) \(0\) \(0\) \(q+(1+\beta _{3})q^{3}-\beta _{2}q^{5}+(-3\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1280.2.f.i \(6\) \(10.221\) 6.0.350464.1 None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
1280.2.f.j \(6\) \(10.221\) 6.0.350464.1 None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\beta _{1})q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
1280.2.f.k \(6\) \(10.221\) 6.0.350464.1 None \(0\) \(4\) \(0\) \(0\) \(q+(1+\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
1280.2.f.l \(6\) \(10.221\) 6.0.350464.1 None \(0\) \(4\) \(0\) \(0\) \(q+(1+\beta _{1})q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)