Properties

Label 1870.2.h
Level 1870
Weight 2
Character orbit h
Rep. character \(\chi_{1870}(1189,\cdot)\)
Character field \(\Q\)
Dimension 92
Newform subspaces 2
Sturm bound 648
Trace bound 3

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1870.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 85 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(648\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1870, [\chi])\).

Total New Old
Modular forms 332 92 240
Cusp forms 316 92 224
Eisenstein series 16 0 16

Trace form

\( 92q - 92q^{4} + 100q^{9} + O(q^{10}) \) \( 92q - 92q^{4} + 100q^{9} - 24q^{15} + 92q^{16} + 48q^{21} + 8q^{25} - 40q^{26} + 24q^{30} + 8q^{35} - 100q^{36} + 92q^{49} - 8q^{50} - 48q^{51} + 88q^{59} + 24q^{60} - 92q^{64} - 16q^{66} + 112q^{69} - 56q^{70} + 156q^{81} - 48q^{84} - 56q^{85} + 56q^{86} - 144q^{89} - 64q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1870, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1870.2.h.a \(46\) \(14.932\) None \(0\) \(-8\) \(0\) \(-8\)
1870.2.h.b \(46\) \(14.932\) None \(0\) \(8\) \(0\) \(8\)

Decomposition of \(S_{2}^{\mathrm{old}}(1870, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1870, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(935, [\chi])\)\(^{\oplus 2}\)