Properties

Label 1440.2.bw
Level $1440$
Weight $2$
Character orbit 1440.bw
Rep. character $\chi_{1440}(191,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $2$
Sturm bound $576$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.bw (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(15\)

Dimensions

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

Total New Old
Modular forms 608 96 512
Cusp forms 544 96 448
Eisenstein series 64 0 64

Trace form

\( 96 q + 8 q^{9} + O(q^{10}) \) \( 96 q + 8 q^{9} - 8 q^{21} + 48 q^{25} - 24 q^{29} + 40 q^{33} + 72 q^{41} - 16 q^{45} + 48 q^{49} + 40 q^{57} + 72 q^{69} - 48 q^{73} + 96 q^{77} + 32 q^{93} - 24 q^{97} + O(q^{100}) \)

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.bw.a 1440.bw 36.h $48$ $11.498$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
1440.2.bw.b 1440.bw 36.h $48$ $11.498$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(1440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)