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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(855))\) 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 5 19
855.2.a.a 855.a 1.a $1$ $6.827$ \(\Q\) None 285.2.a.c \(-1\) \(0\) \(-1\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
855.2.a.b 855.a 1.a $1$ $6.827$ \(\Q\) None 285.2.a.b \(-1\) \(0\) \(1\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}-2q^{7}+3q^{8}-q^{10}+\cdots\)
855.2.a.c 855.a 1.a $1$ $6.827$ \(\Q\) None 285.2.a.a \(1\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
855.2.a.d 855.a 1.a $2$ $6.827$ \(\Q(\sqrt{2}) \) None 285.2.a.g \(-2\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+\beta q^{7}+\cdots\)
855.2.a.e 855.a 1.a $2$ $6.827$ \(\Q(\sqrt{2}) \) None 285.2.a.f \(-2\) \(0\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(2+\cdots)q^{7}+\cdots\)
855.2.a.f 855.a 1.a $2$ $6.827$ \(\Q(\sqrt{3}) \) None 285.2.a.e \(0\) \(0\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-q^{5}+(-1-\beta )q^{7}-\beta q^{8}+\cdots\)
855.2.a.g 855.a 1.a $2$ $6.827$ \(\Q(\sqrt{7}) \) None 285.2.a.d \(0\) \(0\) \(-2\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+5q^{4}-q^{5}+(-1+\beta )q^{7}+\cdots\)
855.2.a.h 855.a 1.a $3$ $6.827$ 3.3.148.1 None 855.2.a.h \(-1\) \(0\) \(-3\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}-\beta _{2}q^{7}+\cdots\)
855.2.a.i 855.a 1.a $3$ $6.827$ 3.3.148.1 None 95.2.a.a \(-1\) \(0\) \(-3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+2\beta _{2}q^{7}+\cdots\)
855.2.a.j 855.a 1.a $3$ $6.827$ 3.3.148.1 None 855.2.a.j \(-1\) \(0\) \(3\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+(-2+\cdots)q^{7}+\cdots\)
855.2.a.k 855.a 1.a $3$ $6.827$ 3.3.148.1 None 855.2.a.j \(1\) \(0\) \(-3\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+(-2+\cdots)q^{7}+\cdots\)
855.2.a.l 855.a 1.a $3$ $6.827$ 3.3.148.1 None 855.2.a.h \(1\) \(0\) \(3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}-\beta _{2}q^{7}+\cdots\)
855.2.a.m 855.a 1.a $4$ $6.827$ 4.4.11344.1 None 95.2.a.b \(2\) \(0\) \(4\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+q^{5}+(2+\cdots)q^{7}+\cdots\)

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

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