↑

Properties

Label 775.2.ca
Level $775$
Weight $2$
Character orbit 775.ca
Rep. character $\chi_{775}(92,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $624$
Newform subspaces $2$
Sturm bound $160$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 775.ca (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 2 \)
Sturm bound: \(160\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(775, [\chi])\).

Total New Old
Modular forms 656 656 0
Cusp forms 624 624 0
Eisenstein series 32 32 0

Trace form

\( 624 q - 16 q^{2} - 20 q^{4} - 16 q^{5} - 8 q^{7} - 30 q^{8} - 20 q^{9} + O(q^{10}) \) \( 624 q - 16 q^{2} - 20 q^{4} - 16 q^{5} - 8 q^{7} - 30 q^{8} - 20 q^{9} - 24 q^{10} - 20 q^{14} + 132 q^{16} - 36 q^{18} - 20 q^{19} - 28 q^{20} + 16 q^{25} + 62 q^{28} - 6 q^{31} - 16 q^{32} + 24 q^{33} + 8 q^{35} + 92 q^{36} - 12 q^{38} - 20 q^{39} - 124 q^{40} - 12 q^{41} - 68 q^{45} + 36 q^{47} - 124 q^{50} - 32 q^{51} - 44 q^{56} - 120 q^{59} - 64 q^{62} - 60 q^{63} + 10 q^{64} - 60 q^{66} - 8 q^{67} + 120 q^{69} - 10 q^{70} - 52 q^{71} - 178 q^{72} - 64 q^{76} + 136 q^{78} + 72 q^{80} + 152 q^{81} - 54 q^{82} + 100 q^{87} + 48 q^{90} - 80 q^{93} - 20 q^{94} + 64 q^{95} - 228 q^{97} - 26 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(775, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
775.2.ca.a 775.ca 775.ba $48$ $6.188$ \(\Q(\sqrt{-31}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{20}]$
775.2.ca.b 775.ca 775.ba $576$ $6.188$ None \(-16\) \(0\) \(-16\) \(-8\) $\mathrm{SU}(2)[C_{20}]$