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Properties

Label 775.2.k
Level $775$
Weight $2$
Character orbit 775.k
Rep. character $\chi_{775}(101,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $188$
Newform subspaces $8$
Sturm bound $160$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 775.k (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 8 \)
Sturm bound: \(160\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 344 212 132
Cusp forms 296 188 108
Eisenstein series 48 24 24

Trace form

\( 188 q + 3 q^{2} + 3 q^{3} - 43 q^{4} - 18 q^{6} + 15 q^{7} - 13 q^{8} - 38 q^{9} + O(q^{10}) \) \( 188 q + 3 q^{2} + 3 q^{3} - 43 q^{4} - 18 q^{6} + 15 q^{7} - 13 q^{8} - 38 q^{9} - 16 q^{11} - 8 q^{12} + 12 q^{13} - 2 q^{14} - 45 q^{16} + 3 q^{17} + 22 q^{18} + 29 q^{19} - 29 q^{21} + 18 q^{22} + 15 q^{23} + 59 q^{24} - 24 q^{26} + 27 q^{27} - 54 q^{28} + 3 q^{29} - 17 q^{31} - 38 q^{32} - 6 q^{33} + 25 q^{34} + 40 q^{36} + 28 q^{37} - 6 q^{38} - 3 q^{39} - 6 q^{41} - 36 q^{42} - 17 q^{43} - 20 q^{44} + 19 q^{46} + 17 q^{47} + 72 q^{48} + 22 q^{49} - 23 q^{51} + 53 q^{52} - q^{53} + 24 q^{54} + 52 q^{56} - 52 q^{57} - 77 q^{58} - 17 q^{59} + 12 q^{61} - 94 q^{62} + 32 q^{63} - 99 q^{64} - 30 q^{66} + 28 q^{67} - 86 q^{68} - 33 q^{69} + 75 q^{71} + 104 q^{72} + 27 q^{73} - 37 q^{74} - 59 q^{76} + 50 q^{77} + 45 q^{78} - 86 q^{79} - 51 q^{81} - 44 q^{82} + 26 q^{83} + 141 q^{84} + 23 q^{86} - 58 q^{87} + 64 q^{88} + 9 q^{89} - 60 q^{91} - 90 q^{92} + 78 q^{93} - 186 q^{94} + 30 q^{96} - 23 q^{97} + 140 q^{98} + 28 q^{99} + O(q^{100}) \)

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.k.a 775.k 31.d $4$ $6.188$ \(\Q(\zeta_{10})\) None \(-2\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2})q^{2}+(1-2\zeta_{10}+\cdots)q^{3}+\cdots\)
775.2.k.b 775.k 31.d $4$ $6.188$ \(\Q(\zeta_{10})\) None \(2\) \(1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2})q^{2}+(-1+2\zeta_{10}+\cdots)q^{3}+\cdots\)
775.2.k.c 775.k 31.d $4$ $6.188$ \(\Q(\zeta_{10})\) None \(3\) \(-1\) \(0\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+\zeta_{10}^{2})q^{2}+(-1+\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
775.2.k.d 775.k 31.d $24$ $6.188$ None \(-2\) \(0\) \(0\) \(9\) $\mathrm{SU}(2)[C_{5}]$
775.2.k.e 775.k 31.d $24$ $6.188$ None \(2\) \(4\) \(0\) \(3\) $\mathrm{SU}(2)[C_{5}]$
775.2.k.f 775.k 31.d $36$ $6.188$ None \(-2\) \(1\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{5}]$
775.2.k.g 775.k 31.d $36$ $6.188$ None \(2\) \(-1\) \(0\) \(6\) $\mathrm{SU}(2)[C_{5}]$
775.2.k.h 775.k 31.d $56$ $6.188$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(775, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(775, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)