Properties

Label 240.3.j
Level $240$
Weight $3$
Character orbit 240.j
Rep. character $\chi_{240}(79,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $3$
Sturm bound $144$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 240.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(240, [\chi])\).

Total New Old
Modular forms 108 12 96
Cusp forms 84 12 72
Eisenstein series 24 0 24

Trace form

\( 12 q - 12 q^{5} + 36 q^{9} + O(q^{10}) \) \( 12 q - 12 q^{5} + 36 q^{9} + 60 q^{25} + 120 q^{29} + 72 q^{41} - 36 q^{45} - 300 q^{49} - 120 q^{61} + 96 q^{65} + 108 q^{81} - 384 q^{85} - 456 q^{89} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(240, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
240.3.j.a 240.j 20.d $4$ $6.540$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{3}-5q^{5}-4\zeta_{12}q^{7}+3q^{9}+\cdots\)
240.3.j.b 240.j 20.d $4$ $6.540$ \(\Q(\sqrt{3}, \sqrt{-7})\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-2+\beta _{2})q^{5}+2\beta _{1}q^{7}+\cdots\)
240.3.j.c 240.j 20.d $4$ $6.540$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{2}q^{3}+(4-\zeta_{12}^{3})q^{5}-2\zeta_{12}^{2}q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(240, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)