Properties

Label 175.4.b
Level $175$
Weight $4$
Character orbit 175.b
Rep. character $\chi_{175}(99,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $6$
Sturm bound $80$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 175.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(80\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(175, [\chi])\).

Total New Old
Modular forms 66 26 40
Cusp forms 54 26 28
Eisenstein series 12 0 12

Trace form

\( 26q - 120q^{4} - 24q^{6} - 294q^{9} + O(q^{10}) \) \( 26q - 120q^{4} - 24q^{6} - 294q^{9} - 80q^{11} + 56q^{14} + 392q^{16} - 96q^{19} - 196q^{21} - 116q^{24} + 452q^{26} + 276q^{29} - 168q^{31} - 1328q^{34} + 2196q^{36} - 560q^{39} + 1568q^{41} + 2726q^{44} - 1526q^{46} - 1274q^{49} - 4036q^{51} + 3868q^{54} - 714q^{56} - 92q^{59} + 3664q^{61} + 1314q^{64} - 2500q^{66} - 3048q^{69} - 3588q^{71} - 8318q^{74} + 1596q^{76} + 5300q^{79} + 1522q^{81} + 2800q^{84} + 2486q^{86} - 1984q^{89} - 224q^{91} + 7108q^{94} - 13428q^{96} - 52q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(175, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
175.4.b.a \(2\) \(10.325\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+8iq^{3}+7q^{4}-8q^{6}+7iq^{7}+\cdots\)
175.4.b.b \(2\) \(10.325\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-2iq^{3}+7q^{4}+2q^{6}+7iq^{7}+\cdots\)
175.4.b.c \(4\) \(10.325\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(4\zeta_{8}-\zeta_{8}^{2})q^{2}+(-\zeta_{8}-4\zeta_{8}^{2})q^{3}+\cdots\)
175.4.b.d \(4\) \(10.325\) \(\Q(i, \sqrt{41})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}-2\beta _{2})q^{3}+(-3+\beta _{3})q^{4}+\cdots\)
175.4.b.e \(6\) \(10.325\) 6.0.3299353600.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{2})q^{2}+(-\beta _{1}+\beta _{2}+\beta _{5})q^{3}+\cdots\)
175.4.b.f \(8\) \(10.325\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{2}+(-\beta _{2}-\beta _{5})q^{3}+(-9+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(175, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)