Properties

Label 1280.3.e
Level $1280$
Weight $3$
Character orbit 1280.e
Rep. character $\chi_{1280}(639,\cdot)$
Character field $\Q$
Dimension $92$
Newform subspaces $12$
Sturm bound $576$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1280 = 2^{8} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1280.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(576\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1280, [\chi])\).

Total New Old
Modular forms 408 100 308
Cusp forms 360 92 268
Eisenstein series 48 8 40

Trace form

\( 92 q - 244 q^{9} + O(q^{10}) \) \( 92 q - 244 q^{9} + 4 q^{25} + 8 q^{41} + 468 q^{49} + 64 q^{65} + 460 q^{81} - 312 q^{89} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1280, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1280.3.e.a \(2\) \(34.877\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-8\) \(0\) \(q+(-4+3i)q^{5}+9q^{9}-24q^{13}+2^{4}iq^{17}+\cdots\)
1280.3.e.b \(2\) \(34.877\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(-8\) \(q+4iq^{3}-5iq^{5}-4q^{7}-7q^{9}+20q^{15}+\cdots\)
1280.3.e.c \(2\) \(34.877\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(8\) \(q+4iq^{3}+5iq^{5}+4q^{7}-7q^{9}-20q^{15}+\cdots\)
1280.3.e.d \(2\) \(34.877\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(8\) \(0\) \(q+(4+3i)q^{5}+9q^{9}+24q^{13}-2^{4}iq^{17}+\cdots\)
1280.3.e.e \(4\) \(34.877\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+5\beta _{1}q^{5}+3\beta _{3}q^{7}-11q^{9}+\cdots\)
1280.3.e.f \(6\) \(34.877\) 6.0.1827904.1 None \(0\) \(0\) \(-8\) \(-12\) \(q+\beta _{1}q^{3}+(-2-\beta _{2}+\beta _{5})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1280.3.e.g \(6\) \(34.877\) 6.0.1827904.1 None \(0\) \(0\) \(-8\) \(12\) \(q+\beta _{1}q^{3}+(-1+\beta _{4})q^{5}+(2+\beta _{4}+\beta _{5})q^{7}+\cdots\)
1280.3.e.h \(6\) \(34.877\) 6.0.1827904.1 None \(0\) \(0\) \(8\) \(-12\) \(q+\beta _{1}q^{3}+(1-\beta _{4})q^{5}+(-2-\beta _{4}-\beta _{5})q^{7}+\cdots\)
1280.3.e.i \(6\) \(34.877\) 6.0.1827904.1 None \(0\) \(0\) \(8\) \(12\) \(q+\beta _{1}q^{3}+(2+\beta _{2}-\beta _{5})q^{5}+(2+\beta _{4}+\cdots)q^{7}+\cdots\)
1280.3.e.j \(8\) \(34.877\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{2}q^{3}+(-\zeta_{24}-\zeta_{24}^{3})q^{5}-3\zeta_{24}^{4}q^{7}+\cdots\)
1280.3.e.k \(24\) \(34.877\) None \(0\) \(0\) \(0\) \(0\)
1280.3.e.l \(24\) \(34.877\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{3}^{\mathrm{old}}(1280, [\chi])\) into lower level spaces

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