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Properties

Label 837.2.a
Level $837$
Weight $2$
Character orbit 837.a
Rep. character $\chi_{837}(1,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $12$
Sturm bound $192$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 837 = 3^{3} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 837.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(192\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(837))\).

Total New Old
Modular forms 102 40 62
Cusp forms 91 40 51
Eisenstein series 11 0 11

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

\(3\)\(31\)FrickeDim
\(+\)\(+\)\(+\)\(9\)
\(+\)\(-\)\(-\)\(11\)
\(-\)\(+\)\(-\)\(11\)
\(-\)\(-\)\(+\)\(9\)
Plus space\(+\)\(18\)
Minus space\(-\)\(22\)

Trace form

\( 40 q + 40 q^{4} + O(q^{10}) \) \( 40 q + 40 q^{4} - 8 q^{10} - 12 q^{13} + 16 q^{16} + 4 q^{19} - 12 q^{22} + 28 q^{25} - 4 q^{28} + 20 q^{34} - 40 q^{37} + 12 q^{40} - 12 q^{43} + 4 q^{46} + 24 q^{49} + 24 q^{52} + 20 q^{55} + 16 q^{58} - 32 q^{61} + 52 q^{64} - 20 q^{67} + 68 q^{70} - 28 q^{73} + 8 q^{76} - 44 q^{79} - 4 q^{82} - 68 q^{85} - 80 q^{88} - 16 q^{91} - 64 q^{94} + 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(837))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 31
837.2.a.a 837.a 1.a $2$ $6.683$ \(\Q(\sqrt{2}) \) None 837.2.a.a \(-2\) \(0\) \(-4\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2q^{5}+\cdots\)
837.2.a.b 837.a 1.a $2$ $6.683$ \(\Q(\sqrt{17}) \) None 837.2.a.b \(-1\) \(0\) \(4\) \(5\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(2+\beta )q^{4}+2q^{5}+(3-\beta )q^{7}+\cdots\)
837.2.a.c 837.a 1.a $2$ $6.683$ \(\Q(\sqrt{3}) \) None 837.2.a.c \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-\beta q^{5}-q^{7}-\beta q^{11}-q^{13}+\cdots\)
837.2.a.d 837.a 1.a $2$ $6.683$ \(\Q(\sqrt{17}) \) None 837.2.a.b \(1\) \(0\) \(-4\) \(5\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(2+\beta )q^{4}-2q^{5}+(3-\beta )q^{7}+\cdots\)
837.2.a.e 837.a 1.a $2$ $6.683$ \(\Q(\sqrt{2}) \) None 837.2.a.a \(2\) \(0\) \(4\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2q^{5}+(1+\cdots)q^{7}+\cdots\)
837.2.a.f 837.a 1.a $3$ $6.683$ 3.3.257.1 None 837.2.a.f \(-1\) \(0\) \(1\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
837.2.a.g 837.a 1.a $3$ $6.683$ 3.3.257.1 None 837.2.a.f \(1\) \(0\) \(-1\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
837.2.a.h 837.a 1.a $4$ $6.683$ \(\Q(\sqrt{2}, \sqrt{5})\) None 837.2.a.h \(0\) \(0\) \(0\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{5}+(-2-\beta _{3})q^{7}+\cdots\)
837.2.a.i 837.a 1.a $4$ $6.683$ \(\Q(\sqrt{2}, \sqrt{5})\) None 837.2.a.i \(0\) \(0\) \(0\) \(-8\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
837.2.a.j 837.a 1.a $5$ $6.683$ 5.5.710984.1 None 837.2.a.j \(-3\) \(0\) \(-5\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
837.2.a.k 837.a 1.a $5$ $6.683$ 5.5.710984.1 None 837.2.a.j \(3\) \(0\) \(5\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
837.2.a.l 837.a 1.a $6$ $6.683$ 6.6.23493568.1 None 837.2.a.l \(0\) \(0\) \(0\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{4}q^{5}+(1+\beta _{5})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(837))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(837)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(279))\)\(^{\oplus 2}\)