Properties

Label 5040.2.k
Level $5040$
Weight $2$
Character orbit 5040.k
Rep. character $\chi_{5040}(1889,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $9$
Sturm bound $2304$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5040.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(2304\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5040, [\chi])\).

Total New Old
Modular forms 1200 96 1104
Cusp forms 1104 96 1008
Eisenstein series 96 0 96

Trace form

\( 96 q + O(q^{10}) \) \( 96 q - 16 q^{25} - 16 q^{49} - 96 q^{79} + 16 q^{85} + 48 q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5040, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5040.2.k.a $4$ $40.245$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{5}+(\beta _{1}+\beta _{2})q^{7}+\beta _{2}q^{11}+(-2\beta _{1}+\cdots)q^{13}+\cdots\)
5040.2.k.b $4$ $40.245$ \(\Q(\sqrt{-2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}-4\beta _{1}q^{11}+\cdots\)
5040.2.k.c $4$ $40.245$ \(\Q(\sqrt{-2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}+(-\beta _{1}-\beta _{3})q^{7}-4\beta _{1}q^{11}+\cdots\)
5040.2.k.d $4$ $40.245$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{5}+(\beta _{1}-2\beta _{2})q^{7}+\beta _{2}q^{11}+\cdots\)
5040.2.k.e $8$ $40.245$ 8.0.\(\cdots\).11 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}-\beta _{5}q^{7}+(\beta _{5}+\beta _{6})q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots\)
5040.2.k.f $8$ $40.245$ 8.0.\(\cdots\).11 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{5}+\beta _{6}-\beta _{7})q^{5}+\cdots\)
5040.2.k.g $16$ $40.245$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}+\beta _{9}q^{7}-\beta _{6}q^{11}-\beta _{14}q^{13}+\cdots\)
5040.2.k.h $24$ $40.245$ None \(0\) \(0\) \(0\) \(0\)
5040.2.k.i $24$ $40.245$ None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(5040, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5040, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1260, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1680, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2520, [\chi])\)\(^{\oplus 2}\)