Properties

Label 240.2.h
Level $240$
Weight $2$
Character orbit 240.h
Rep. character $\chi_{240}(191,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $96$
Trace bound $9$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(240, [\chi])\).

Total New Old
Modular forms 60 8 52
Cusp forms 36 8 28
Eisenstein series 24 0 24

Trace form

\( 8 q + 12 q^{9} + O(q^{10}) \) \( 8 q + 12 q^{9} + 8 q^{13} - 12 q^{21} - 8 q^{25} - 8 q^{37} + 12 q^{45} - 16 q^{49} - 24 q^{57} - 8 q^{61} - 36 q^{69} - 64 q^{73} + 48 q^{93} + 80 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(240, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
240.2.h.a 240.h 12.b $4$ $1.916$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(\beta _{1}+\beta _{3})q^{7}+3\beta _{2}q^{9}+\cdots\)
240.2.h.b 240.h 12.b $4$ $1.916$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{3}q^{3}-\zeta_{12}q^{5}+2\zeta_{12}^{2}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)