Properties

Label 861.2.h
Level 861
Weight 2
Character orbit h
Rep. character \(\chi_{861}(778,\cdot)\)
Character field \(\Q\)
Dimension 40
Newforms 2
Sturm bound 224
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 861 = 3 \cdot 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 861.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 41 \)
Character field: \(\Q\)
Newforms: \( 2 \)
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 116 40 76
Cusp forms 108 40 68
Eisenstein series 8 0 8

Trace form

\( 40q - 4q^{2} + 36q^{4} + 16q^{5} - 12q^{8} - 40q^{9} + O(q^{10}) \) \( 40q - 4q^{2} + 36q^{4} + 16q^{5} - 12q^{8} - 40q^{9} - 8q^{10} + 44q^{16} + 4q^{18} + 40q^{20} + 4q^{21} + 24q^{25} - 12q^{31} + 12q^{32} + 12q^{33} - 36q^{36} + 12q^{37} + 16q^{39} + 8q^{40} - 32q^{41} - 4q^{42} + 20q^{43} - 16q^{45} - 40q^{49} - 60q^{50} - 12q^{51} - 16q^{57} + 32q^{59} - 20q^{61} - 24q^{62} + 92q^{64} - 32q^{66} + 12q^{72} + 44q^{73} - 128q^{74} - 40q^{78} + 72q^{80} + 40q^{81} + 16q^{83} + 12q^{84} - 32q^{86} + 28q^{87} + 8q^{90} + 8q^{91} - 128q^{92} + 4q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(861, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
861.2.h.a \(18\) \(6.875\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(12\) \(0\) \(q+\beta _{5}q^{2}+\beta _{4}q^{3}+(1-\beta _{2})q^{4}+(1-\beta _{14}+\cdots)q^{5}+\cdots\)
861.2.h.b \(22\) \(6.875\) None \(-4\) \(0\) \(4\) \(0\)

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

\( S_{2}^{\mathrm{old}}(861, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(123, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 2}\)