Properties

Label 240.2.s
Level $240$
Weight $2$
Character orbit 240.s
Rep. character $\chi_{240}(61,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $32$
Newform subspaces $3$
Sturm bound $96$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 104 32 72
Cusp forms 88 32 56
Eisenstein series 16 0 16

Trace form

\( 32q + 8q^{4} + O(q^{10}) \) \( 32q + 8q^{4} - 4q^{10} + 16q^{11} - 8q^{14} + 8q^{15} - 4q^{16} - 8q^{18} + 8q^{19} - 16q^{20} + 16q^{22} - 4q^{24} - 16q^{28} + 32q^{29} - 40q^{32} - 36q^{34} + 4q^{36} + 32q^{37} - 40q^{38} - 16q^{43} + 8q^{44} + 12q^{46} - 32q^{49} + 8q^{50} - 8q^{51} - 56q^{52} - 32q^{53} - 4q^{54} + 48q^{56} + 64q^{58} - 32q^{59} - 16q^{61} - 48q^{62} - 16q^{63} - 16q^{64} - 24q^{66} - 16q^{67} - 8q^{68} - 16q^{69} + 16q^{70} + 8q^{72} + 32q^{74} - 4q^{76} - 32q^{77} - 24q^{78} - 16q^{79} - 32q^{81} + 40q^{82} + 48q^{84} + 16q^{85} + 48q^{86} + 8q^{88} - 16q^{91} + 104q^{92} + 52q^{94} + 40q^{96} + 16q^{98} + 16q^{99} + O(q^{100}) \)

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.s.a \(4\) \(1.916\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+\zeta_{8}^{3}q^{3}+2q^{4}+\cdots\)
240.2.s.b \(8\) \(1.916\) 8.0.18939904.2 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{6}q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
240.2.s.c \(20\) \(1.916\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+\beta _{2}q^{4}+\beta _{5}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)