Properties

Label 650.2.n
Level $650$
Weight $2$
Character orbit 650.n
Rep. character $\chi_{650}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $6$
Sturm bound $210$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 650.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(210\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(650, [\chi])\).

Total New Old
Modular forms 232 40 192
Cusp forms 184 40 144
Eisenstein series 48 0 48

Trace form

\( 40q - 20q^{4} + 8q^{9} + O(q^{10}) \) \( 40q - 20q^{4} + 8q^{9} + 12q^{11} + 24q^{14} - 20q^{16} + 24q^{19} + 12q^{26} + 8q^{36} + 92q^{39} - 96q^{41} - 24q^{46} - 4q^{49} + 48q^{51} - 36q^{54} - 12q^{56} - 84q^{59} + 28q^{61} + 40q^{64} - 48q^{66} + 12q^{69} - 36q^{74} - 24q^{76} - 40q^{79} - 44q^{81} - 36q^{84} + 96q^{89} - 84q^{91} + 12q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(650, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
650.2.n.a \(4\) \(5.190\) \(\Q(\zeta_{12})\) None \(-2\) \(-6\) \(0\) \(-6\) \(q+(-1+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
650.2.n.b \(4\) \(5.190\) \(\Q(\zeta_{12})\) None \(2\) \(6\) \(0\) \(6\) \(q+\zeta_{12}^{2}q^{2}+(2-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
650.2.n.c \(8\) \(5.190\) 8.0.22581504.2 None \(-4\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
650.2.n.d \(8\) \(5.190\) 8.0.22581504.2 None \(-4\) \(6\) \(0\) \(0\) \(q+(-1-\beta _{6})q^{2}+(1+\beta _{2})q^{3}+\beta _{6}q^{4}+\cdots\)
650.2.n.e \(8\) \(5.190\) 8.0.22581504.2 None \(4\) \(-6\) \(0\) \(0\) \(q+(1-\beta _{2})q^{2}+(\beta _{4}+\beta _{6})q^{3}-\beta _{2}q^{4}+\cdots\)
650.2.n.f \(8\) \(5.190\) 8.0.22581504.2 None \(4\) \(0\) \(0\) \(0\) \(q+(1-\beta _{6})q^{2}+(\beta _{3}+\beta _{5}+\beta _{7})q^{3}-\beta _{6}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(650, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(650, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)