Properties

Label 650.2.m
Level $650$
Weight $2$
Character orbit 650.m
Rep. character $\chi_{650}(101,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $44$
Newform subspaces $5$
Sturm bound $210$
Trace bound $6$

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Defining parameters

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

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

\( 44q + 22q^{4} - 18q^{9} + O(q^{10}) \) \( 44q + 22q^{4} - 18q^{9} + 12q^{11} - 12q^{13} + 8q^{14} - 22q^{16} - 24q^{19} + 14q^{26} - 24q^{27} - 6q^{29} + 60q^{33} + 18q^{36} + 12q^{37} + 24q^{38} + 4q^{39} - 30q^{41} + 12q^{42} - 24q^{46} + 22q^{49} - 16q^{51} - 48q^{53} - 36q^{54} + 4q^{56} - 12q^{58} + 12q^{59} - 6q^{61} - 24q^{62} - 48q^{63} - 44q^{64} + 16q^{66} - 24q^{67} - 20q^{69} - 24q^{72} - 22q^{74} - 24q^{76} + 24q^{77} - 12q^{78} + 8q^{79} + 2q^{81} + 36q^{84} - 24q^{87} + 24q^{89} + 20q^{91} - 36q^{93} - 12q^{94} - 36q^{97} + 48q^{98} + O(q^{100}) \)

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.m.a \(4\) \(5.190\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(-1+\zeta_{12}+\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+\cdots\)
650.2.m.b \(8\) \(5.190\) 8.0.22581504.2 None \(0\) \(-2\) \(0\) \(-6\) \(q-\beta _{7}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\)
650.2.m.c \(8\) \(5.190\) 8.0.22581504.2 None \(0\) \(2\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{4}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots\)
650.2.m.d \(8\) \(5.190\) 8.0.22581504.2 None \(0\) \(2\) \(0\) \(6\) \(q+\beta _{7}q^{2}+(2-\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\)
650.2.m.e \(16\) \(5.190\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{6})q^{2}-\beta _{5}q^{3}-\beta _{8}q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(650, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)