Properties

Label 175.2.a
Level $175$
Weight $2$
Character orbit 175.a
Rep. character $\chi_{175}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $6$
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: \(\Q\)
Newform subspaces: \( 6 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(175))\) into newform subspaces

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

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