↑

Properties

Label 861.2.n
Level $861$
Weight $2$
Character orbit 861.n
Rep. character $\chi_{861}(379,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $160$
Newform subspaces $6$
Sturm bound $224$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 861 = 3 \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 861.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 6 \)
Sturm bound: \(224\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(861, [\chi])\).

Total New Old
Modular forms 464 160 304
Cusp forms 432 160 272
Eisenstein series 32 0 32

Trace form

\( 160 q + 4 q^{2} - 36 q^{4} + 16 q^{5} + 12 q^{8} + 160 q^{9} + O(q^{10}) \) \( 160 q + 4 q^{2} - 36 q^{4} + 16 q^{5} + 12 q^{8} + 160 q^{9} - 16 q^{10} + 8 q^{11} + 16 q^{12} + 32 q^{13} - 12 q^{15} - 12 q^{16} + 20 q^{17} + 4 q^{18} + 8 q^{19} - 60 q^{20} + 4 q^{21} + 4 q^{22} - 24 q^{23} + 4 q^{25} - 36 q^{26} + 40 q^{29} + 24 q^{30} - 8 q^{31} - 72 q^{32} + 12 q^{33} + 4 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 224 q^{38} + 16 q^{39} - 8 q^{40} + 20 q^{41} - 16 q^{42} + 44 q^{43} + 72 q^{44} + 16 q^{45} + 8 q^{46} - 28 q^{47} - 48 q^{48} - 40 q^{49} - 40 q^{50} + 28 q^{51} - 20 q^{52} + 16 q^{53} - 56 q^{55} - 4 q^{57} + 32 q^{58} + 32 q^{59} + 32 q^{60} + 20 q^{61} + 96 q^{62} - 52 q^{64} - 56 q^{65} - 8 q^{66} + 36 q^{67} + 152 q^{68} - 24 q^{69} + 8 q^{70} - 40 q^{71} + 12 q^{72} + 24 q^{73} - 164 q^{74} + 48 q^{75} + 36 q^{76} - 64 q^{78} - 80 q^{79} - 188 q^{80} + 160 q^{81} - 192 q^{82} - 24 q^{83} + 12 q^{84} + 8 q^{85} - 80 q^{86} - 80 q^{87} - 8 q^{88} + 80 q^{89} - 16 q^{90} - 56 q^{91} + 72 q^{92} - 44 q^{93} - 64 q^{94} + 16 q^{95} + 40 q^{96} - 60 q^{97} + 4 q^{98} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(861, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
861.2.n.a 861.n 41.d $4$ $6.875$ \(\Q(\zeta_{10})\) None \(3\) \(-4\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}^{3})q^{2}-q^{3}+(1-\zeta_{10})q^{4}+\cdots\)
861.2.n.b 861.n 41.d $8$ $6.875$ 8.0.511890625.1 None \(3\) \(8\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{5}q^{2}+q^{3}+(\beta _{3}-\beta _{5}-\beta _{7})q^{4}+\cdots\)
861.2.n.c 861.n 41.d $28$ $6.875$ None \(-1\) \(28\) \(3\) \(-7\) $\mathrm{SU}(2)[C_{5}]$
861.2.n.d 861.n 41.d $36$ $6.875$ None \(2\) \(-36\) \(7\) \(9\) $\mathrm{SU}(2)[C_{5}]$
861.2.n.e 861.n 41.d $40$ $6.875$ None \(-3\) \(-40\) \(6\) \(-10\) $\mathrm{SU}(2)[C_{5}]$
861.2.n.f 861.n 41.d $44$ $6.875$ None \(0\) \(44\) \(-3\) \(11\) $\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(861, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(861, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(123, [\chi])\)\(^{\oplus 2}\)