Properties

Label 637.2.e
Level $637$
Weight $2$
Character orbit 637.e
Rep. character $\chi_{637}(79,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $15$
Sturm bound $130$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 15 \)
Sturm bound: \(130\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(3\), \(5\)

Dimensions

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

Total New Old
Modular forms 148 80 68
Cusp forms 116 80 36
Eisenstein series 32 0 32

Trace form

\( 80q + 4q^{2} - 36q^{4} + 2q^{5} - 12q^{8} - 44q^{9} + O(q^{10}) \) \( 80q + 4q^{2} - 36q^{4} + 2q^{5} - 12q^{8} - 44q^{9} - 10q^{10} + 6q^{11} - 10q^{12} - 4q^{13} + 20q^{15} - 12q^{16} - 4q^{17} + 10q^{18} + 8q^{19} - 32q^{20} - 68q^{22} - 2q^{23} + 20q^{24} - 34q^{25} + 6q^{26} - 4q^{29} + 30q^{30} + 4q^{31} + 46q^{32} + 8q^{33} + 32q^{34} + 4q^{36} + 24q^{37} - 26q^{38} + 8q^{40} - 28q^{41} + 12q^{43} + 18q^{44} - 32q^{45} + 52q^{46} + 2q^{47} + 76q^{48} - 76q^{50} - 20q^{51} + 6q^{52} + 26q^{53} + 18q^{54} - 30q^{58} + 10q^{59} - 24q^{60} - 12q^{61} + 76q^{62} - 28q^{64} + 4q^{65} + 6q^{66} + 24q^{67} - 18q^{68} - 56q^{69} - 60q^{71} + 28q^{72} + 22q^{73} - 10q^{74} - 20q^{75} - 48q^{76} + 20q^{78} + 34q^{79} + 70q^{80} - 72q^{81} + 44q^{82} - 12q^{83} - 60q^{85} + 14q^{86} - 28q^{87} - 4q^{89} + 88q^{90} + 140q^{92} + 66q^{93} + 46q^{94} + 22q^{95} - 22q^{96} + 68q^{97} + 72q^{99} + O(q^{100}) \)

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.e.a \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-3q^{8}+3\zeta_{6}q^{9}+\cdots\)
637.2.e.b \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-3\) \(0\) \(q+(-2+2\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
637.2.e.c \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(3\) \(0\) \(q+(2-2\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
637.2.e.d \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-3\) \(0\) \(q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
637.2.e.e \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(3\) \(0\) \(q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
637.2.e.f \(4\) \(5.086\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(-6\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-3+\beta _{1}+\cdots)q^{5}+\cdots\)
637.2.e.g \(4\) \(5.086\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(6\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(3-\beta _{1}+\cdots)q^{5}+\cdots\)
637.2.e.h \(4\) \(5.086\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(3\) \(0\) \(0\) \(0\) \(q+(1+\beta _{1}+\beta _{3})q^{2}+(2\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\cdots\)
637.2.e.i \(6\) \(5.086\) 6.0.2696112.1 None \(-1\) \(-2\) \(2\) \(0\) \(q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
637.2.e.j \(6\) \(5.086\) 6.0.2696112.1 None \(-1\) \(2\) \(-2\) \(0\) \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
637.2.e.k \(6\) \(5.086\) 6.0.4406832.1 None \(2\) \(-4\) \(-5\) \(0\) \(q+(\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(-1+\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
637.2.e.l \(6\) \(5.086\) 6.0.4406832.1 None \(2\) \(4\) \(5\) \(0\) \(q+(\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(1-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
637.2.e.m \(10\) \(5.086\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(0\) \(2\) \(0\) \(q+(\beta _{1}-\beta _{7})q^{2}+(\beta _{4}-\beta _{9})q^{3}+(-2+\cdots)q^{4}+\cdots\)
637.2.e.n \(12\) \(5.086\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-8\) \(-6\) \(0\) \(q+(-\beta _{3}+\beta _{11})q^{2}+(\beta _{1}+\beta _{2}-\beta _{8}+\cdots)q^{3}+\cdots\)
637.2.e.o \(12\) \(5.086\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(8\) \(6\) \(0\) \(q+(-\beta _{3}+\beta _{11})q^{2}+(-\beta _{1}-\beta _{2}+\beta _{8}+\cdots)q^{3}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(637, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)