Properties

Label 2880.2.k
Level $2880$
Weight $2$
Character orbit 2880.k
Rep. character $\chi_{2880}(1441,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $12$
Sturm bound $1152$
Trace bound $47$

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Defining parameters

Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2880.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(1152\)
Trace bound: \(47\)
Distinguishing \(T_p\): \(7\), \(11\), \(23\), \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2880, [\chi])\).

Total New Old
Modular forms 624 40 584
Cusp forms 528 40 488
Eisenstein series 96 0 96

Trace form

\( 40 q + O(q^{10}) \) \( 40 q - 40 q^{25} - 48 q^{41} + 8 q^{49} + 32 q^{73} + 48 q^{89} - 32 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2880, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2880.2.k.a $2$ $22.997$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q-iq^{5}-4q^{7}-4iq^{11}-2iq^{13}+\cdots\)
2880.2.k.b $2$ $22.997$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{5}+6iq^{13}+2iq^{19}-6q^{23}+\cdots\)
2880.2.k.c $2$ $22.997$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}-6iq^{13}+2iq^{19}+6q^{23}+\cdots\)
2880.2.k.d $2$ $22.997$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q+iq^{5}+4q^{7}-4iq^{11}+2iq^{13}+\cdots\)
2880.2.k.e $4$ $22.997$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-12\) \(q-\zeta_{12}q^{5}+(-3-\zeta_{12}^{3})q^{7}+2\zeta_{12}^{2}q^{11}+\cdots\)
2880.2.k.f $4$ $22.997$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-8\) \(q-\zeta_{12}q^{5}-2q^{7}+(-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{11}+\cdots\)
2880.2.k.g $4$ $22.997$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}^{2}q^{11}+\cdots\)
2880.2.k.h $4$ $22.997$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{5}-\zeta_{12}^{2}q^{11}-\zeta_{12}^{2}q^{13}+\cdots\)
2880.2.k.i $4$ $22.997$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{5}+\zeta_{12}^{2}q^{11}-\zeta_{12}^{2}q^{13}+\cdots\)
2880.2.k.j $4$ $22.997$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}^{2}q^{11}+\cdots\)
2880.2.k.k $4$ $22.997$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) \(q-\zeta_{12}q^{5}+2q^{7}+(2\zeta_{12}-\zeta_{12}^{2})q^{11}+\cdots\)
2880.2.k.l $4$ $22.997$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(12\) \(q-\zeta_{12}q^{5}+(3+\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2880, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)