Properties

Label 175.2.e
Level 175
Weight 2
Character orbit e
Rep. character \(\chi_{175}(51,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 20
Newforms 5
Sturm bound 40
Trace bound 2

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Defining parameters

Level: \( N \) = \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 175.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 5 \)
Sturm bound: \(40\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(175, [\chi])\).

Total New Old
Modular forms 52 32 20
Cusp forms 28 20 8
Eisenstein series 24 12 12

Trace form

\(20q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 22q^{14} \) \(\mathstrut +\mathstrut 6q^{16} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 8q^{18} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut 12q^{24} \) \(\mathstrut -\mathstrut 22q^{26} \) \(\mathstrut -\mathstrut 4q^{27} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut -\mathstrut 8q^{29} \) \(\mathstrut -\mathstrut 2q^{31} \) \(\mathstrut -\mathstrut 6q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 36q^{36} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut 2q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 8q^{49} \) \(\mathstrut -\mathstrut 14q^{51} \) \(\mathstrut -\mathstrut 20q^{52} \) \(\mathstrut -\mathstrut 8q^{53} \) \(\mathstrut +\mathstrut 38q^{54} \) \(\mathstrut -\mathstrut 18q^{56} \) \(\mathstrut +\mathstrut 16q^{57} \) \(\mathstrut -\mathstrut 2q^{58} \) \(\mathstrut -\mathstrut 2q^{59} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut +\mathstrut 24q^{62} \) \(\mathstrut -\mathstrut 64q^{64} \) \(\mathstrut -\mathstrut 48q^{66} \) \(\mathstrut +\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 20q^{68} \) \(\mathstrut +\mathstrut 48q^{69} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut +\mathstrut 46q^{74} \) \(\mathstrut +\mathstrut 68q^{76} \) \(\mathstrut -\mathstrut 28q^{77} \) \(\mathstrut -\mathstrut 8q^{78} \) \(\mathstrut -\mathstrut 6q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 22q^{84} \) \(\mathstrut +\mathstrut 40q^{86} \) \(\mathstrut -\mathstrut 2q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 38q^{91} \) \(\mathstrut -\mathstrut 12q^{92} \) \(\mathstrut -\mathstrut 12q^{93} \) \(\mathstrut +\mathstrut 30q^{94} \) \(\mathstrut -\mathstrut 14q^{96} \) \(\mathstrut -\mathstrut 24q^{97} \) \(\mathstrut +\mathstrut 14q^{98} \) \(\mathstrut -\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(175, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
175.2.e.a \(2\) \(1.397\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-1\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
175.2.e.b \(2\) \(1.397\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
175.2.e.c \(4\) \(1.397\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(2\) \(0\) \(-2\) \(q+(1+\beta _{1}+\beta _{2})q^{2}+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots\)
175.2.e.d \(6\) \(1.397\) 6.0.1783323.2 None \(-1\) \(3\) \(0\) \(2\) \(q-\beta _{1}q^{2}+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
175.2.e.e \(6\) \(1.397\) 6.0.1783323.2 None \(1\) \(-3\) \(0\) \(-2\) \(q+\beta _{1}q^{2}+(-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(175, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)