Properties

Label 1280.2.d
Level $1280$
Weight $2$
Character orbit 1280.d
Rep. character $\chi_{1280}(641,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $13$
Sturm bound $384$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 1280 = 2^{8} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1280.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(384\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\), \(31\)

Dimensions

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

Total New Old
Modular forms 216 32 184
Cusp forms 168 32 136
Eisenstein series 48 0 48

Trace form

\( 32q - 32q^{9} + O(q^{10}) \) \( 32q - 32q^{9} - 32q^{25} - 32q^{49} + 64q^{57} + 64q^{73} + 32q^{81} - 64q^{97} + O(q^{100}) \)

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

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

\( S_{2}^{\mathrm{old}}(1280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)