Properties

Label 775.2.a
Level $775$
Weight $2$
Character orbit 775.a
Rep. character $\chi_{775}(1,\cdot)$
Character field $\Q$
Dimension $47$
Newform subspaces $12$
Sturm bound $160$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 775.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(160\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(775))\).

Total New Old
Modular forms 86 47 39
Cusp forms 75 47 28
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.

\(5\)\(31\)FrickeDim.
\(+\)\(+\)\(+\)\(10\)
\(+\)\(-\)\(-\)\(13\)
\(-\)\(+\)\(-\)\(15\)
\(-\)\(-\)\(+\)\(9\)
Plus space\(+\)\(19\)
Minus space\(-\)\(28\)

Trace form

\( 47 q + 2 q^{2} + 2 q^{3} + 48 q^{4} - 2 q^{6} + 3 q^{8} + 43 q^{9} + O(q^{10}) \) \( 47 q + 2 q^{2} + 2 q^{3} + 48 q^{4} - 2 q^{6} + 3 q^{8} + 43 q^{9} - 4 q^{11} + 8 q^{12} - 12 q^{13} - 3 q^{14} + 50 q^{16} - 8 q^{17} - 2 q^{18} - 4 q^{19} - 26 q^{21} + 22 q^{22} - 10 q^{23} - 14 q^{24} + 4 q^{26} + 8 q^{27} + 9 q^{28} + 12 q^{29} - 3 q^{31} + 28 q^{32} + 16 q^{33} + 20 q^{34} + 40 q^{36} + 2 q^{37} + 21 q^{38} - 32 q^{39} - 4 q^{41} + 26 q^{42} - 18 q^{43} - 10 q^{44} + 26 q^{46} + 28 q^{47} - 2 q^{48} + 13 q^{49} + 8 q^{51} - 38 q^{52} - 14 q^{53} - 4 q^{54} + 38 q^{56} - 18 q^{57} - 18 q^{58} + 12 q^{59} - 32 q^{61} + 4 q^{62} + 8 q^{63} + 39 q^{64} - 8 q^{67} - 34 q^{68} - 12 q^{69} - 20 q^{71} + 11 q^{72} - 22 q^{73} + 32 q^{74} - 51 q^{76} - 20 q^{77} - 40 q^{78} + 6 q^{79} - 29 q^{81} - 61 q^{82} + 44 q^{83} - 156 q^{84} - 8 q^{86} - 12 q^{87} + 36 q^{88} - 44 q^{89} - 30 q^{91} - 20 q^{92} + 2 q^{93} - 104 q^{94} - 140 q^{96} + 8 q^{97} - 35 q^{98} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(775))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 31
775.2.a.a 775.a 1.a $1$ $6.188$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-2q^{9}-4q^{11}-2q^{12}+\cdots\)
775.2.a.b 775.a 1.a $1$ $6.188$ \(\Q\) None \(1\) \(-2\) \(0\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}-q^{4}-2q^{6}-4q^{7}-3q^{8}+\cdots\)
775.2.a.c 775.a 1.a $1$ $6.188$ \(\Q\) None \(2\) \(1\) \(0\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+2q^{7}+\cdots\)
775.2.a.d 775.a 1.a $2$ $6.188$ \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(0\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+2\beta q^{3}+(-1+\beta )q^{4}+(-2+\cdots)q^{6}+\cdots\)
775.2.a.e 775.a 1.a $4$ $6.188$ 4.4.8468.1 None \(-1\) \(-1\) \(0\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\cdots\)
775.2.a.f 775.a 1.a $4$ $6.188$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{3})q^{2}-\beta _{1}q^{3}+(-1-\beta _{2}+\cdots)q^{6}+\cdots\)
775.2.a.g 775.a 1.a $4$ $6.188$ 4.4.20308.1 None \(1\) \(1\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\cdots\)
775.2.a.h 775.a 1.a $5$ $6.188$ 5.5.144209.1 None \(-4\) \(-3\) \(0\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
775.2.a.i 775.a 1.a $5$ $6.188$ 5.5.205225.1 None \(-4\) \(-1\) \(0\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+\beta _{3}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
775.2.a.j 775.a 1.a $5$ $6.188$ 5.5.205225.1 None \(4\) \(1\) \(0\) \(6\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
775.2.a.k 775.a 1.a $5$ $6.188$ 5.5.144209.1 None \(4\) \(3\) \(0\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
775.2.a.l 775.a 1.a $10$ $6.188$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{4}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(775))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(775)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 2}\)