Properties

Label 1080.2.k
Level $1080$
Weight $2$
Character orbit 1080.k
Rep. character $\chi_{1080}(541,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $4$
Sturm bound $432$
Trace bound $8$

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Defining parameters

Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1080.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(432\)
Trace bound: \(8\)
Distinguishing \(T_p\): \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1080, [\chi])\).

Total New Old
Modular forms 228 64 164
Cusp forms 204 64 140
Eisenstein series 24 0 24

Trace form

\( 64 q - 2 q^{4} + O(q^{10}) \) \( 64 q - 2 q^{4} + 2 q^{10} - 30 q^{16} + 44 q^{22} - 64 q^{25} + 44 q^{28} - 8 q^{31} + 6 q^{34} + 16 q^{40} + 30 q^{46} + 48 q^{49} + 28 q^{52} - 48 q^{58} + 16 q^{64} - 12 q^{70} + 16 q^{73} - 34 q^{76} + 136 q^{79} - 4 q^{82} - 52 q^{88} + 24 q^{94} - 16 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1080, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1080.2.k.a 1080.k 8.b $12$ $8.624$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{9}q^{2}-\beta _{8}q^{4}-\beta _{7}q^{5}+(-\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots\)
1080.2.k.b 1080.k 8.b $16$ $8.624$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{9}q^{2}-\beta _{2}q^{4}-\beta _{7}q^{5}-\beta _{14}q^{7}+\cdots\)
1080.2.k.c 1080.k 8.b $16$ $8.624$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{8}q^{5}-\beta _{11}q^{7}+\cdots\)
1080.2.k.d 1080.k 8.b $20$ $8.624$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+\beta _{4}q^{4}-\beta _{6}q^{5}-\beta _{12}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1080, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1080, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)