Properties

Label 637.2.a
Level $637$
Weight $2$
Character orbit 637.a
Rep. character $\chi_{637}(1,\cdot)$
Character field $\Q$
Dimension $41$
Newform subspaces $14$
Sturm bound $130$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(130\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(2\), \(3\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(637))\).

Total New Old
Modular forms 72 41 31
Cusp forms 57 41 16
Eisenstein series 15 0 15

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(9\)
\(+\)\(-\)\(-\)\(11\)
\(-\)\(+\)\(-\)\(12\)
\(-\)\(-\)\(+\)\(9\)
Plus space\(+\)\(18\)
Minus space\(-\)\(23\)

Trace form

\( 41q - q^{2} + 4q^{3} + 43q^{4} - 2q^{5} - 9q^{8} + 45q^{9} + O(q^{10}) \) \( 41q - q^{2} + 4q^{3} + 43q^{4} - 2q^{5} - 9q^{8} + 45q^{9} - 2q^{10} + 8q^{12} - q^{13} + 4q^{15} + 43q^{16} - 2q^{17} - q^{18} + 12q^{19} + 2q^{20} - 16q^{22} - 16q^{23} + 4q^{24} + 23q^{25} - 3q^{26} + 4q^{27} - 26q^{29} - 36q^{30} + 4q^{31} - 49q^{32} + 4q^{33} - 2q^{34} + 27q^{36} - 10q^{37} + 8q^{38} + 4q^{39} + 10q^{40} - 2q^{41} - 4q^{43} - 24q^{44} - 22q^{45} - 16q^{46} - 8q^{47} - 12q^{48} - 35q^{50} - 16q^{51} + q^{52} - 2q^{53} - 48q^{54} - 12q^{55} - 16q^{57} - 42q^{58} - 16q^{59} + 14q^{61} + 8q^{62} + 23q^{64} + 2q^{65} - 12q^{66} - 4q^{67} - 42q^{68} + 20q^{69} + 12q^{71} - 49q^{72} + 22q^{73} - 50q^{74} + 48q^{75} - 16q^{76} - 8q^{78} - 32q^{79} + 38q^{80} + 49q^{81} - 14q^{82} - 24q^{83} - 24q^{85} + 64q^{86} + 16q^{87} - 12q^{88} - 26q^{89} + 50q^{90} + 76q^{92} - 28q^{93} + 20q^{94} - 40q^{95} + 4q^{96} + 6q^{97} + 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(637))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 13
637.2.a.a \(1\) \(5.086\) \(\Q\) None \(-2\) \(0\) \(3\) \(0\) \(-\) \(-\) \(q-2q^{2}+2q^{4}+3q^{5}-3q^{9}-6q^{10}+\cdots\)
637.2.a.b \(1\) \(5.086\) \(\Q\) None \(0\) \(2\) \(3\) \(0\) \(-\) \(+\) \(q+2q^{3}-2q^{4}+3q^{5}+q^{9}-4q^{12}+\cdots\)
637.2.a.c \(1\) \(5.086\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q+q^{2}-q^{4}-3q^{8}-3q^{9}-3q^{11}+\cdots\)
637.2.a.d \(1\) \(5.086\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q+q^{2}-q^{4}-3q^{8}-3q^{9}-3q^{11}+\cdots\)
637.2.a.e \(2\) \(5.086\) \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q+(-1-\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
637.2.a.f \(2\) \(5.086\) \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q+(-1-\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}+\cdots\)
637.2.a.g \(2\) \(5.086\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-6\) \(0\) \(-\) \(-\) \(q+\beta q^{2}+\beta q^{3}+(-3-\beta )q^{5}+2q^{6}+\cdots\)
637.2.a.h \(3\) \(5.086\) 3.3.404.1 None \(-2\) \(-4\) \(-5\) \(0\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(2+\cdots)q^{4}+\cdots\)
637.2.a.i \(3\) \(5.086\) 3.3.404.1 None \(-2\) \(4\) \(5\) \(0\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
637.2.a.j \(3\) \(5.086\) 3.3.316.1 None \(1\) \(2\) \(-2\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
637.2.a.k \(5\) \(5.086\) 5.5.746052.1 None \(4\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
637.2.a.l \(5\) \(5.086\) 5.5.746052.1 None \(4\) \(0\) \(2\) \(0\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}-\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
637.2.a.m \(6\) \(5.086\) 6.6.4507648.1 None \(0\) \(-8\) \(-6\) \(0\) \(+\) \(+\) \(q-\beta _{2}q^{2}+(-1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)
637.2.a.n \(6\) \(5.086\) 6.6.4507648.1 None \(0\) \(8\) \(6\) \(0\) \(+\) \(-\) \(q-\beta _{2}q^{2}+(1+\beta _{1})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(637))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(637)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 2}\)