Properties

Label 2880.3.l
Level $2880$
Weight $3$
Character orbit 2880.l
Rep. character $\chi_{2880}(1601,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $12$
Sturm bound $1728$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2880.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(1728\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2880, [\chi])\).

Total New Old
Modular forms 1200 64 1136
Cusp forms 1104 64 1040
Eisenstein series 96 0 96

Trace form

\( 64 q + O(q^{10}) \) \( 64 q - 64 q^{13} - 320 q^{25} + 320 q^{37} + 448 q^{49} - 384 q^{61} - 320 q^{85} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2880, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2880.3.l.a 2880.l 3.b $4$ $78.474$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(-32\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}+(-8+\beta _{3})q^{7}+(\beta _{1}+6\beta _{2}+\cdots)q^{11}+\cdots\)
2880.3.l.b 2880.l 3.b $4$ $78.474$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{5}+(-4+\beta _{3})q^{7}+(-\beta _{1}+6\beta _{2}+\cdots)q^{11}+\cdots\)
2880.3.l.c 2880.l 3.b $4$ $78.474$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}+(-4-\beta _{3})q^{7}+(7\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots\)
2880.3.l.d 2880.l 3.b $4$ $78.474$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{5}-\beta _{3}q^{7}+(\beta _{1}-2\beta _{2})q^{11}+\cdots\)
2880.3.l.e 2880.l 3.b $4$ $78.474$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{5}+\beta _{3}q^{7}+(-\beta _{1}+2\beta _{2})q^{11}+\cdots\)
2880.3.l.f 2880.l 3.b $4$ $78.474$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{5}+(4-\beta _{3})q^{7}+(\beta _{1}-6\beta _{2})q^{11}+\cdots\)
2880.3.l.g 2880.l 3.b $4$ $78.474$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}+(4+\beta _{3})q^{7}+(-7\beta _{1}+2\beta _{2}+\cdots)q^{11}+\cdots\)
2880.3.l.h 2880.l 3.b $4$ $78.474$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(32\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}+(8+\beta _{3})q^{7}+(\beta _{1}-6\beta _{2})q^{11}+\cdots\)
2880.3.l.i 2880.l 3.b $8$ $78.474$ 8.0.\(\cdots\).9 None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{5}+(-2-\beta _{1})q^{7}+(2\beta _{5}+\beta _{7})q^{11}+\cdots\)
2880.3.l.j 2880.l 3.b $8$ $78.474$ 8.0.\(\cdots\).4 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{5}-\beta _{5}q^{7}-\beta _{6}q^{11}+(-10+\cdots)q^{13}+\cdots\)
2880.3.l.k 2880.l 3.b $8$ $78.474$ 8.0.\(\cdots\).14 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{5}+\beta _{1}q^{7}-\beta _{7}q^{11}+(6-\beta _{2}+\cdots)q^{13}+\cdots\)
2880.3.l.l 2880.l 3.b $8$ $78.474$ 8.0.\(\cdots\).9 None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{5}+(2-\beta _{1})q^{7}+(-2\beta _{5}+\beta _{7})q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(2880, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 20}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 14}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)