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Properties

Label 5472.2.j
Level $5472$
Weight $2$
Character orbit 5472.j
Rep. character $\chi_{5472}(4751,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $4$
Sturm bound $1920$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5472.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(1920\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5472, [\chi])\).

Total New Old
Modular forms 992 72 920
Cusp forms 928 72 856
Eisenstein series 64 0 64

Trace form

\( 72 q + O(q^{10}) \) \( 72 q + 72 q^{25} + 64 q^{43} - 72 q^{49} - 32 q^{67} + 96 q^{91} - 32 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(5472, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5472.2.j.a 5472.j 24.f $4$ $43.694$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}-\zeta_{8}^{2}q^{11}+3\zeta_{8}q^{13}+\cdots\)
5472.2.j.b 5472.j 24.f $4$ $43.694$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}-\beta _{3}q^{7}-\beta _{1}q^{11}-5\beta _{1}q^{17}+\cdots\)
5472.2.j.c 5472.j 24.f $28$ $43.694$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
5472.2.j.d 5472.j 24.f $36$ $43.694$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(5472, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5472, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)