Properties

Label 2640.2.d
Level $2640$
Weight $2$
Character orbit 2640.d
Rep. character $\chi_{2640}(529,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $11$
Sturm bound $1152$
Trace bound $21$

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Defining parameters

Level: \( N \) \(=\) \( 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2640.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(1152\)
Trace bound: \(21\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2640, [\chi])\).

Total New Old
Modular forms 600 60 540
Cusp forms 552 60 492
Eisenstein series 48 0 48

Trace form

\( 60 q - 4 q^{5} - 60 q^{9} + O(q^{10}) \) \( 60 q - 4 q^{5} - 60 q^{9} - 8 q^{19} - 4 q^{25} + 8 q^{29} - 16 q^{31} + 24 q^{35} + 8 q^{41} + 4 q^{45} - 60 q^{49} + 8 q^{51} - 16 q^{59} - 24 q^{61} + 16 q^{65} + 16 q^{69} + 16 q^{71} + 40 q^{79} + 60 q^{81} - 40 q^{89} + 16 q^{91} - 24 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2640, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2640.2.d.a 2640.d 5.b $2$ $21.081$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-1-2i)q^{5}+2iq^{7}-q^{9}+\cdots\)
2640.2.d.b 2640.d 5.b $2$ $21.081$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+(1-2i)q^{5}-q^{9}-q^{11}-4iq^{13}+\cdots\)
2640.2.d.c 2640.d 5.b $4$ $21.081$ \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{7}+\cdots\)
2640.2.d.d 2640.d 5.b $4$ $21.081$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
2640.2.d.e 2640.d 5.b $4$ $21.081$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}^{2}q^{3}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)
2640.2.d.f 2640.d 5.b $6$ $21.081$ 6.0.350464.1 None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
2640.2.d.g 2640.d 5.b $6$ $21.081$ 6.0.350464.1 None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}+(\beta _{1}+\beta _{5})q^{5}+(\beta _{1}+\beta _{4})q^{7}+\cdots\)
2640.2.d.h 2640.d 5.b $6$ $21.081$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(-\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)
2640.2.d.i 2640.d 5.b $6$ $21.081$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(\beta _{1}+3\beta _{4}+\cdots)q^{7}+\cdots\)
2640.2.d.j 2640.d 5.b $10$ $21.081$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}-\beta _{2}q^{5}-\beta _{9}q^{7}-q^{9}-q^{11}+\cdots\)
2640.2.d.k 2640.d 5.b $10$ $21.081$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+\beta _{5}q^{5}-\beta _{1}q^{7}-q^{9}+q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2640, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(660, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1320, [\chi])\)\(^{\oplus 2}\)