Properties

Label 637.2.q
Level $637$
Weight $2$
Character orbit 637.q
Rep. character $\chi_{637}(491,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $86$
Newform subspaces $10$
Sturm bound $130$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 10 \)
Sturm bound: \(130\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(637, [\chi])\).

Total New Old
Modular forms 148 106 42
Cusp forms 116 86 30
Eisenstein series 32 20 12

Trace form

\( 86q + 3q^{2} + 2q^{3} + 39q^{4} + 12q^{6} - 35q^{9} + O(q^{10}) \) \( 86q + 3q^{2} + 2q^{3} + 39q^{4} + 12q^{6} - 35q^{9} - 9q^{10} - 6q^{11} + 8q^{12} + q^{13} - 36q^{15} - 29q^{16} + q^{17} + 6q^{19} + 9q^{20} - 12q^{22} + 4q^{23} - 6q^{24} - 40q^{25} + 39q^{26} - 4q^{27} - 11q^{29} + 38q^{30} - 27q^{32} + 30q^{33} + 31q^{36} - 15q^{37} - 16q^{38} - 6q^{39} - 98q^{40} - 21q^{41} - 16q^{43} + 3q^{45} - 6q^{46} - 8q^{48} + 78q^{50} + 12q^{51} - 4q^{52} + 14q^{53} - 24q^{54} + 6q^{55} - 93q^{58} - 30q^{59} - 13q^{61} - 2q^{62} + 38q^{64} + 11q^{65} + 52q^{66} + 42q^{67} + 11q^{68} - 16q^{69} - 24q^{71} + 45q^{72} - 21q^{74} - 42q^{75} + 24q^{76} - 42q^{78} + 96q^{79} + 87q^{80} - 23q^{81} - 23q^{82} + 27q^{85} + 8q^{87} + 38q^{88} + 24q^{89} - 30q^{90} - 40q^{92} + 60q^{93} + 2q^{94} + 56q^{95} - 18q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(637, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
637.2.q.a \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(-3\) \(2\) \(0\) \(0\) \(q+(-1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
637.2.q.b \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(3\) \(-1\) \(0\) \(0\) \(q+(1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
637.2.q.c \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(3\) \(1\) \(0\) \(0\) \(q+(1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
637.2.q.d \(4\) \(5.086\) \(\Q(\sqrt{-3}, \sqrt{-13})\) None \(-6\) \(0\) \(0\) \(0\) \(q+(-2+\beta _{2})q^{2}+(1-\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
637.2.q.e \(4\) \(5.086\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(3\) \(-1\) \(0\) \(0\) \(q+(1-\beta _{3})q^{2}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots\)
637.2.q.f \(4\) \(5.086\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(3\) \(1\) \(0\) \(0\) \(q+(1-\beta _{3})q^{2}+(-1+2\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\cdots\)
637.2.q.g \(12\) \(5.086\) 12.0.\(\cdots\).1 None \(0\) \(-3\) \(0\) \(0\) \(q+\beta _{10}q^{2}+(\beta _{1}+\beta _{4}+\beta _{6})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
637.2.q.h \(12\) \(5.086\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{8}q^{2}+(-\beta _{4}-\beta _{9})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.q.i \(12\) \(5.086\) 12.0.\(\cdots\).1 None \(0\) \(3\) \(0\) \(0\) \(q+\beta _{10}q^{2}+(-\beta _{1}-\beta _{4}-\beta _{6})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
637.2.q.j \(32\) \(5.086\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(637, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(637, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)