Properties

Label 640.2.c
Level $640$
Weight $2$
Character orbit 640.c
Rep. character $\chi_{640}(129,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $4$
Sturm bound $192$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 640 = 2^{7} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 640.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(192\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(11\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(640, [\chi])\).

Total New Old
Modular forms 112 24 88
Cusp forms 80 24 56
Eisenstein series 32 0 32

Trace form

\( 24 q - 24 q^{9} + O(q^{10}) \) \( 24 q - 24 q^{9} - 8 q^{25} + 16 q^{41} - 24 q^{49} - 32 q^{65} - 8 q^{81} + 80 q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(640, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
640.2.c.a 640.c 5.b $6$ $5.110$ 6.0.350464.1 None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(\beta _{2}+\beta _{5})q^{5}+(\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
640.2.c.b 640.c 5.b $6$ $5.110$ 6.0.350464.1 None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
640.2.c.c 640.c 5.b $6$ $5.110$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{5})q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
640.2.c.d 640.c 5.b $6$ $5.110$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(640, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)