Properties

Label 190.2.b
Level $190$
Weight $2$
Character orbit 190.b
Rep. character $\chi_{190}(39,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $2$
Sturm bound $60$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 190 = 2 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 190.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(60\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(190, [\chi])\).

Total New Old
Modular forms 34 10 24
Cusp forms 26 10 16
Eisenstein series 8 0 8

Trace form

\( 10q - 10q^{4} + 2q^{5} - 10q^{9} + O(q^{10}) \) \( 10q - 10q^{4} + 2q^{5} - 10q^{9} + 4q^{14} - 4q^{15} + 10q^{16} - 2q^{19} - 2q^{20} - 16q^{21} - 6q^{25} + 4q^{26} + 28q^{29} - 12q^{30} + 16q^{31} + 8q^{34} - 4q^{35} + 10q^{36} - 16q^{39} + 4q^{41} + 26q^{45} - 20q^{46} - 10q^{49} + 8q^{50} - 8q^{51} - 4q^{56} + 8q^{59} + 4q^{60} - 20q^{61} - 10q^{64} + 12q^{65} + 8q^{66} - 16q^{70} - 64q^{71} - 28q^{74} + 56q^{75} + 2q^{76} - 8q^{79} + 2q^{80} - 38q^{81} + 16q^{84} - 12q^{85} + 12q^{86} + 28q^{89} + 12q^{90} + 64q^{91} + 28q^{94} - 2q^{95} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(190, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
190.2.b.a \(4\) \(1.517\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}+(\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
190.2.b.b \(6\) \(1.517\) 6.0.5161984.1 None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{4}q^{2}+(\beta _{4}+\beta _{5})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(190, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(190, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)