Properties

Label 650.2.o
Level $650$
Weight $2$
Character orbit 650.o
Rep. character $\chi_{650}(399,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $44$
Newform subspaces $8$
Sturm bound $210$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 650.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(210\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

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

Total New Old
Modular forms 236 44 192
Cusp forms 188 44 144
Eisenstein series 48 0 48

Trace form

\( 44q + 22q^{4} + 34q^{9} + O(q^{10}) \) \( 44q + 22q^{4} + 34q^{9} + 12q^{11} - 24q^{14} - 22q^{16} + 16q^{19} + 8q^{21} - 14q^{26} + 22q^{29} + 32q^{31} + 52q^{34} - 34q^{36} - 20q^{39} + 10q^{41} + 24q^{44} + 14q^{49} - 16q^{51} - 12q^{54} - 12q^{56} - 20q^{59} - 2q^{61} - 44q^{64} + 16q^{66} - 36q^{69} - 48q^{71} - 6q^{74} - 16q^{76} - 56q^{79} - 46q^{81} + 4q^{84} - 24q^{86} + 20q^{89} + 76q^{91} + 28q^{94} + 64q^{99} + O(q^{100}) \)

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.o.a \(4\) \(5.190\) \(\Q(\zeta_{12})\) None \(0\) \(-6\) \(0\) \(12\) \(q+\zeta_{12}q^{2}+(-1+\zeta_{12}-\zeta_{12}^{2})q^{3}+\cdots\)
650.2.o.b \(4\) \(5.190\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}-2\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}-2\zeta_{12}^{2}q^{6}+\cdots\)
650.2.o.c \(4\) \(5.190\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-4\zeta_{12}+4\zeta_{12}^{3})q^{7}+\cdots\)
650.2.o.d \(4\) \(5.190\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(3\zeta_{12}-3\zeta_{12}^{3})q^{7}+\cdots\)
650.2.o.e \(4\) \(5.190\) \(\Q(\zeta_{12})\) None \(0\) \(6\) \(0\) \(-12\) \(q+\zeta_{12}q^{2}+(1+\zeta_{12}+\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
650.2.o.f \(8\) \(5.190\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{3})q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{7})q^{3}+\cdots\)
650.2.o.g \(8\) \(5.190\) 8.0.3317760000.2 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{5}q^{3}+(1-\beta _{2})q^{4}+\cdots\)
650.2.o.h \(8\) \(5.190\) 8.0.592240896.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(1-\beta _{3})q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots\)

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

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