↑

Properties

Label 240.3.bg
Level $240$
Weight $3$
Character orbit 240.bg
Rep. character $\chi_{240}(97,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
Newform subspaces $5$
Sturm bound $144$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 240.bg (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 5 \)
Sturm bound: \(144\)
Trace bound: \(5\)
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 24 192
Cusp forms 168 24 144
Eisenstein series 48 0 48

Trace form

\( 24 q + O(q^{10}) \) \( 24 q + 24 q^{13} - 8 q^{17} + 96 q^{23} + 24 q^{25} + 64 q^{31} + 48 q^{33} + 96 q^{35} + 8 q^{37} - 32 q^{41} - 64 q^{43} - 24 q^{45} - 192 q^{47} - 96 q^{51} - 56 q^{53} - 96 q^{55} + 32 q^{61} - 56 q^{65} + 480 q^{67} + 256 q^{71} - 232 q^{73} - 216 q^{81} - 544 q^{83} + 56 q^{85} - 288 q^{87} - 768 q^{91} + 96 q^{93} - 576 q^{95} + 56 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bg.a 240.bg 5.c $4$ $6.540$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(-1-\beta _{1}-3\beta _{2}+2\beta _{3})q^{5}+\cdots\)
240.3.bg.b 240.bg 5.c $4$ $6.540$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(2\beta _{1}+\beta _{2}-2\beta _{3})q^{5}+(4+\cdots)q^{7}+\cdots\)
240.3.bg.c 240.bg 5.c $4$ $6.540$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(4\) \(12\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(1-\beta _{1}+3\beta _{2}+2\beta _{3})q^{5}+\cdots\)
240.3.bg.d 240.bg 5.c $4$ $6.540$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(12\) \(-20\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(3-\beta _{1}+\beta _{2}-2\beta _{3})q^{5}+\cdots\)
240.3.bg.e 240.bg 5.c $8$ $6.540$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-12\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{4}q^{3}+(-1+\beta _{4}-\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)