Properties

Label 1440.2.k
Level $1440$
Weight $2$
Character orbit 1440.k
Rep. character $\chi_{1440}(721,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $6$
Sturm bound $576$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(576\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1440, [\chi])\).

Total New Old
Modular forms 320 20 300
Cusp forms 256 20 236
Eisenstein series 64 0 64

Trace form

\( 20 q + 4 q^{7} + O(q^{10}) \) \( 20 q + 4 q^{7} - 20 q^{23} - 20 q^{25} - 8 q^{31} + 8 q^{41} + 20 q^{47} + 36 q^{49} + 8 q^{55} - 8 q^{71} - 16 q^{73} + 16 q^{79} - 8 q^{89} + 16 q^{95} + 16 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1440, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1440.2.k.a 1440.k 8.b $2$ $11.498$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{5}-2q^{7}-4iq^{11}+6q^{17}+4iq^{19}+\cdots\)
1440.2.k.b 1440.k 8.b $2$ $11.498$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}+4q^{7}-2iq^{11}-6iq^{13}+\cdots\)
1440.2.k.c 1440.k 8.b $2$ $11.498$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}+4q^{7}-2iq^{11}+6iq^{13}+\cdots\)
1440.2.k.d 1440.k 8.b $4$ $11.498$ \(\Q(i, \sqrt{7})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{5}-2q^{7}+2\beta _{1}q^{11}+\beta _{3}q^{19}+\cdots\)
1440.2.k.e 1440.k 8.b $4$ $11.498$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{5}+(1-\zeta_{12}^{3})q^{7}-2\zeta_{12}q^{11}+\cdots\)
1440.2.k.f 1440.k 8.b $6$ $11.498$ 6.0.399424.1 None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{5}+(-1+\beta _{3})q^{7}+(\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1440, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)