Properties

Label 858.2.a
Level $858$
Weight $2$
Character orbit 858.a
Rep. character $\chi_{858}(1,\cdot)$
Character field $\Q$
Dimension $21$
Newform subspaces $17$
Sturm bound $336$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 858 = 2 \cdot 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 858.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(336\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(858))\).

Total New Old
Modular forms 176 21 155
Cusp forms 161 21 140
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.

\(2\)\(3\)\(11\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(3\)
Plus space\(+\)\(7\)
Minus space\(-\)\(14\)

Trace form

\( 21q + q^{2} + q^{3} + 21q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + 21q^{9} + O(q^{10}) \) \( 21q + q^{2} + q^{3} + 21q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + 21q^{9} + 6q^{10} + q^{11} + q^{12} + q^{13} + 8q^{14} + 6q^{15} + 21q^{16} + 2q^{17} + q^{18} + 4q^{19} + 6q^{20} + 8q^{21} + q^{22} - 8q^{23} + q^{24} + 35q^{25} + q^{26} + q^{27} + 8q^{28} - 34q^{29} + 6q^{30} + q^{32} - 3q^{33} - 6q^{34} - 32q^{35} + 21q^{36} + 6q^{37} - 28q^{38} + q^{39} + 6q^{40} - 22q^{41} - 20q^{43} + q^{44} + 6q^{45} + 8q^{46} + q^{48} + 21q^{49} - q^{50} + 18q^{51} + q^{52} - 10q^{53} + q^{54} + 6q^{55} + 8q^{56} + 20q^{57} + 14q^{58} - 52q^{59} + 6q^{60} + 46q^{61} + 8q^{63} + 21q^{64} - 10q^{65} + q^{66} + 12q^{67} + 2q^{68} - 24q^{71} + q^{72} - 6q^{73} - 10q^{74} - q^{75} + 4q^{76} - 8q^{77} - 3q^{78} - 24q^{79} + 6q^{80} + 21q^{81} + 26q^{82} - 44q^{83} + 8q^{84} - 4q^{85} - 4q^{86} + 6q^{87} + q^{88} + 10q^{89} + 6q^{90} - 8q^{92} - 8q^{93} + 8q^{94} - 40q^{95} + q^{96} - 22q^{97} - 7q^{98} + q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(858))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 11 13
858.2.a.a \(1\) \(6.851\) \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
858.2.a.b \(1\) \(6.851\) \(\Q\) None \(-1\) \(1\) \(-2\) \(4\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+4q^{7}+\cdots\)
858.2.a.c \(1\) \(6.851\) \(\Q\) None \(-1\) \(1\) \(0\) \(-4\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-4q^{7}-q^{8}+\cdots\)
858.2.a.d \(1\) \(6.851\) \(\Q\) None \(-1\) \(1\) \(3\) \(-1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{7}+\cdots\)
858.2.a.e \(1\) \(6.851\) \(\Q\) None \(1\) \(-1\) \(-3\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
858.2.a.f \(1\) \(6.851\) \(\Q\) None \(1\) \(-1\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
858.2.a.g \(1\) \(6.851\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-3\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-3q^{7}+\cdots\)
858.2.a.h \(1\) \(6.851\) \(\Q\) None \(1\) \(-1\) \(2\) \(4\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots\)
858.2.a.i \(1\) \(6.851\) \(\Q\) None \(1\) \(-1\) \(4\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{8}+\cdots\)
858.2.a.j \(1\) \(6.851\) \(\Q\) None \(1\) \(1\) \(-3\) \(5\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+5q^{7}+\cdots\)
858.2.a.k \(1\) \(6.851\) \(\Q\) None \(1\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
858.2.a.l \(1\) \(6.851\) \(\Q\) None \(1\) \(1\) \(2\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
858.2.a.m \(1\) \(6.851\) \(\Q\) None \(1\) \(1\) \(4\) \(-4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}-4q^{7}+\cdots\)
858.2.a.n \(2\) \(6.851\) \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(-3\) \(-1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
858.2.a.o \(2\) \(6.851\) \(\Q(\sqrt{33}) \) None \(-2\) \(-2\) \(1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-\beta q^{7}+\cdots\)
858.2.a.p \(2\) \(6.851\) \(\Q(\sqrt{41}) \) None \(-2\) \(2\) \(-1\) \(3\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}+(2-\beta )q^{7}+\cdots\)
858.2.a.q \(2\) \(6.851\) \(\Q(\sqrt{41}) \) None \(2\) \(2\) \(4\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(858))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(858)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(429))\)\(^{\oplus 2}\)