Properties

Label 175.2.b
Level $175$
Weight $2$
Character orbit 175.b
Rep. character $\chi_{175}(99,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $3$
Sturm bound $40$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(40\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 26 10 16
Cusp forms 14 10 4
Eisenstein series 12 0 12

Trace form

\( 10q - 4q^{4} - 8q^{6} - 14q^{9} + O(q^{10}) \) \( 10q - 4q^{4} - 8q^{6} - 14q^{9} + 4q^{11} - 4q^{14} + 8q^{16} + 8q^{19} + 28q^{24} - 28q^{29} - 20q^{31} + 36q^{34} - 20q^{36} + 28q^{39} + 8q^{41} - 6q^{44} - 34q^{46} - 10q^{49} - 4q^{51} - 24q^{54} + 18q^{56} - 4q^{59} + 16q^{61} - 6q^{64} + 8q^{66} + 12q^{69} + 40q^{71} + 6q^{74} - 52q^{76} + 20q^{79} + 18q^{81} + 4q^{84} + 42q^{86} - 48q^{89} - 4q^{91} - 52q^{94} + 20q^{96} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(175, [\chi])\) into newform subspaces

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

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

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