Properties

Label 185.2.f
Level $185$
Weight $2$
Character orbit 185.f
Rep. character $\chi_{185}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $34$
Newform subspaces $4$
Sturm bound $38$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 185 = 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 185.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(38\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(185, [\chi])\).

Total New Old
Modular forms 42 42 0
Cusp forms 34 34 0
Eisenstein series 8 8 0

Trace form

\( 34q + 4q^{3} - 30q^{4} - 6q^{5} - 4q^{6} - 4q^{7} + O(q^{10}) \) \( 34q + 4q^{3} - 30q^{4} - 6q^{5} - 4q^{6} - 4q^{7} - 6q^{10} - 32q^{12} + 12q^{14} + 10q^{15} + 14q^{16} - 20q^{17} - 22q^{18} + 4q^{19} - 8q^{20} + 20q^{22} + 36q^{24} + 10q^{25} - 20q^{27} - 8q^{28} + 14q^{29} - 8q^{30} + 8q^{33} - 26q^{35} - 12q^{37} - 60q^{38} + 4q^{39} + 18q^{40} + 64q^{42} + 30q^{45} + 40q^{46} + 12q^{47} + 60q^{48} + 24q^{50} - 4q^{51} - 10q^{53} + 40q^{54} + 18q^{55} - 28q^{56} - 22q^{58} - 8q^{59} - 104q^{60} - 10q^{61} - 32q^{62} + 36q^{63} - 38q^{64} + 32q^{65} + 16q^{66} + 8q^{67} + 8q^{68} - 40q^{69} - 20q^{70} + 8q^{71} + 70q^{72} + 30q^{73} + 34q^{74} + 20q^{75} - 36q^{77} - 36q^{78} - 40q^{79} - 8q^{80} - 18q^{81} - 4q^{82} - 24q^{83} - 20q^{85} + 88q^{86} - 64q^{87} - 24q^{88} - 34q^{89} - 4q^{90} + 52q^{91} + 52q^{94} + 20q^{95} - 88q^{96} + 56q^{97} - 102q^{98} - 64q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(185, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
185.2.f.a \(2\) \(1.477\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(-6\) \(q-iq^{2}+(-1-i)q^{3}+q^{4}+(-2+i)q^{5}+\cdots\)
185.2.f.b \(2\) \(1.477\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(-4\) \(0\) \(q-iq^{2}+(2+2i)q^{3}+q^{4}+(-2+i)q^{5}+\cdots\)
185.2.f.c \(6\) \(1.477\) 6.0.350464.1 None \(0\) \(-2\) \(2\) \(-4\) \(q-\beta _{5}q^{2}+(-1+\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
185.2.f.d \(24\) \(1.477\) None \(0\) \(4\) \(0\) \(6\)