Properties

Label 240.2.v
Level $240$
Weight $2$
Character orbit 240.v
Rep. character $\chi_{240}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
Newform subspaces $5$
Sturm bound $96$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 5 \)
Sturm bound: \(96\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\)

Dimensions

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

Total New Old
Modular forms 120 28 92
Cusp forms 72 20 52
Eisenstein series 48 8 40

Trace form

\( 20q + 2q^{3} + 4q^{7} + O(q^{10}) \) \( 20q + 2q^{3} + 4q^{7} - 4q^{13} + 14q^{15} - 12q^{21} - 4q^{25} + 14q^{27} + 4q^{33} - 20q^{37} - 12q^{43} - 12q^{45} - 20q^{51} - 40q^{55} + 20q^{57} - 24q^{61} - 48q^{63} - 20q^{67} + 4q^{73} - 38q^{75} + 4q^{81} - 20q^{85} - 20q^{87} + 56q^{91} - 8q^{93} + 4q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
240.2.v.a \(4\) \(1.916\) \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(4\) \(4\) \(q+(-1+\zeta_{8}^{2})q^{3}+(1+2\zeta_{8})q^{5}+(1+\cdots)q^{7}+\cdots\)
240.2.v.b \(4\) \(1.916\) \(\Q(i, \sqrt{5})\) None \(0\) \(-2\) \(0\) \(4\) \(q+(-1+\beta _{3})q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+\cdots\)
240.2.v.c \(4\) \(1.916\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(4\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+(-1-2\zeta_{8})q^{5}+(1+\cdots)q^{7}+\cdots\)
240.2.v.d \(4\) \(1.916\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(-12\) \(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
240.2.v.e \(4\) \(1.916\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(4\) \(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)