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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
185.2.f.a 185.f 185.f $2$ $1.477$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q-iq^{2}+(-1-i)q^{3}+q^{4}+(-2+i)q^{5}+\cdots\)
185.2.f.b 185.f 185.f $2$ $1.477$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-iq^{2}+(2+2i)q^{3}+q^{4}+(-2+i)q^{5}+\cdots\)
185.2.f.c 185.f 185.f $6$ $1.477$ 6.0.350464.1 None \(0\) \(-2\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{2}+(-1+\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
185.2.f.d 185.f 185.f $24$ $1.477$ None \(0\) \(4\) \(0\) \(6\) $\mathrm{SU}(2)[C_{4}]$