Properties

Label 855.2.a
Level $855$
Weight $2$
Character orbit 855.a
Rep. character $\chi_{855}(1,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $13$
Sturm bound $240$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(240\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(855))\).

Total New Old
Modular forms 128 30 98
Cusp forms 113 30 83
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.

\(3\)\(5\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(7\)
Plus space\(+\)\(11\)
Minus space\(-\)\(19\)

Trace form

\( 30q - 4q^{2} + 26q^{4} + 2q^{5} - 4q^{7} + O(q^{10}) \) \( 30q - 4q^{2} + 26q^{4} + 2q^{5} - 4q^{7} - 8q^{11} - 4q^{13} + 12q^{14} + 10q^{16} + 4q^{17} - 2q^{20} + 16q^{22} + 12q^{23} + 30q^{25} + 28q^{26} + 12q^{28} - 4q^{29} + 8q^{31} + 16q^{32} + 24q^{34} + 4q^{35} - 8q^{37} + 6q^{38} + 4q^{41} + 4q^{43} - 24q^{44} + 4q^{46} + 4q^{47} + 14q^{49} - 4q^{50} - 28q^{52} - 16q^{53} + 8q^{55} + 44q^{56} - 24q^{58} - 32q^{59} + 4q^{61} + 8q^{62} - 38q^{64} - 4q^{67} + 68q^{68} - 20q^{70} + 4q^{73} - 4q^{74} + 24q^{77} - 16q^{79} + 6q^{80} - 16q^{82} + 28q^{83} - 20q^{85} + 20q^{86} + 44q^{88} + 12q^{89} + 16q^{91} - 44q^{92} - 4q^{94} + 8q^{95} + 16q^{97} - 52q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(855))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 19
855.2.a.a \(1\) \(6.827\) \(\Q\) None \(-1\) \(0\) \(-1\) \(4\) \(-\) \(+\) \(+\) \(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
855.2.a.b \(1\) \(6.827\) \(\Q\) None \(-1\) \(0\) \(1\) \(-2\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{4}+q^{5}-2q^{7}+3q^{8}-q^{10}+\cdots\)
855.2.a.c \(1\) \(6.827\) \(\Q\) None \(1\) \(0\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
855.2.a.d \(2\) \(6.827\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+\beta q^{7}+\cdots\)
855.2.a.e \(2\) \(6.827\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(4\) \(-\) \(-\) \(-\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(2+\cdots)q^{7}+\cdots\)
855.2.a.f \(2\) \(6.827\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(-\) \(q+\beta q^{2}+q^{4}-q^{5}+(-1-\beta )q^{7}-\beta q^{8}+\cdots\)
855.2.a.g \(2\) \(6.827\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(q+\beta q^{2}+5q^{4}-q^{5}+(-1+\beta )q^{7}+\cdots\)
855.2.a.h \(3\) \(6.827\) 3.3.148.1 None \(-1\) \(0\) \(-3\) \(0\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}-\beta _{2}q^{7}+\cdots\)
855.2.a.i \(3\) \(6.827\) 3.3.148.1 None \(-1\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+2\beta _{2}q^{7}+\cdots\)
855.2.a.j \(3\) \(6.827\) 3.3.148.1 None \(-1\) \(0\) \(3\) \(-4\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+(-2+\cdots)q^{7}+\cdots\)
855.2.a.k \(3\) \(6.827\) 3.3.148.1 None \(1\) \(0\) \(-3\) \(-4\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+(-2+\cdots)q^{7}+\cdots\)
855.2.a.l \(3\) \(6.827\) 3.3.148.1 None \(1\) \(0\) \(3\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}-\beta _{2}q^{7}+\cdots\)
855.2.a.m \(4\) \(6.827\) 4.4.11344.1 None \(2\) \(0\) \(4\) \(4\) \(-\) \(-\) \(-\) \(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+q^{5}+(2+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(855))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(855)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 2}\)