Properties

Label 175.2.a
Level 175
Weight 2
Character orbit a
Rep. character \(\chi_{175}(1,\cdot)\)
Character field \(\Q\)
Dimension 9
Newforms 6
Sturm bound 40
Trace bound 3

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Defining parameters

Level: \( N \) = \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 175.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(40\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(175))\).

Total New Old
Modular forms 26 9 17
Cusp forms 15 9 6
Eisenstein series 11 0 11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(7\)

Trace form

\(9q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 10q^{13} \) \(\mathstrut -\mathstrut q^{14} \) \(\mathstrut -\mathstrut 7q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 7q^{18} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 7q^{28} \) \(\mathstrut +\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 9q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 31q^{36} \) \(\mathstrut -\mathstrut 14q^{37} \) \(\mathstrut -\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 22q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut +\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 28q^{48} \) \(\mathstrut +\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut +\mathstrut 6q^{52} \) \(\mathstrut -\mathstrut 10q^{53} \) \(\mathstrut -\mathstrut 8q^{54} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 26q^{58} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut -\mathstrut 9q^{64} \) \(\mathstrut +\mathstrut 10q^{68} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 5q^{72} \) \(\mathstrut +\mathstrut 6q^{73} \) \(\mathstrut +\mathstrut 8q^{74} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut +\mathstrut 4q^{77} \) \(\mathstrut +\mathstrut 20q^{78} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 33q^{81} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut +\mathstrut 14q^{86} \) \(\mathstrut -\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 54q^{89} \) \(\mathstrut -\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 4q^{93} \) \(\mathstrut +\mathstrut 12q^{94} \) \(\mathstrut +\mathstrut 8q^{96} \) \(\mathstrut +\mathstrut 10q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut +\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(175))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 7
175.2.a.a \(1\) \(1.397\) \(\Q\) None \(-2\) \(-1\) \(0\) \(1\) \(-\) \(-\) \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{7}-2q^{9}+\cdots\)
175.2.a.b \(1\) \(1.397\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(q-q^{3}-2q^{4}-q^{7}-2q^{9}-3q^{11}+\cdots\)
175.2.a.c \(1\) \(1.397\) \(\Q\) None \(2\) \(1\) \(0\) \(-1\) \(-\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}-q^{7}-2q^{9}+\cdots\)
175.2.a.d \(2\) \(1.397\) \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(0\) \(-2\) \(-\) \(+\) \(q-\beta q^{2}+(2-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
175.2.a.e \(2\) \(1.397\) \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(0\) \(2\) \(+\) \(-\) \(q+\beta q^{2}+(-2+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
175.2.a.f \(2\) \(1.397\) \(\Q(\sqrt{17}) \) None \(1\) \(1\) \(0\) \(2\) \(+\) \(-\) \(q+\beta q^{2}+(1-\beta )q^{3}+(2+\beta )q^{4}-4q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(175))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(175)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)