↑

Properties

Label 240.3.bj
Level $240$
Weight $3$
Character orbit 240.bj
Rep. character $\chi_{240}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $48$
Newform subspaces $3$
Sturm bound $144$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 240.bj (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 60 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 216 48 168
Cusp forms 168 48 120
Eisenstein series 48 0 48

Trace form

\( 48 q + 48 q^{21} + 96 q^{37} + 96 q^{57} - 336 q^{73} - 48 q^{81} - 672 q^{85} - 336 q^{93} - 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
240.3.bj.a 240.bj 60.l $8$ $6.540$ \(\Q(\zeta_{24})\) None 240.3.bj.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta_{7}+\beta_{6}+\beta_{4})q^{3}+5\beta_1 q^{5}+\cdots\)
240.3.bj.b 240.bj 60.l $16$ $6.540$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 240.3.bj.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{4}q^{7}+(\beta _{7}-\beta _{9}+\cdots)q^{9}+\cdots\)
240.3.bj.c 240.bj 60.l $24$ $6.540$ None 240.3.bj.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{3}^{\mathrm{old}}(240, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)