Properties

Label 175.3.j
Level $175$
Weight $3$
Character orbit 175.j
Rep. character $\chi_{175}(24,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $44$
Newform subspaces $2$
Sturm bound $60$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 175.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(60\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(175, [\chi])\).

Total New Old
Modular forms 92 52 40
Cusp forms 68 44 24
Eisenstein series 24 8 16

Trace form

\( 44 q + 42 q^{4} - 32 q^{9} + O(q^{10}) \) \( 44 q + 42 q^{4} - 32 q^{9} - 8 q^{11} + 74 q^{14} - 50 q^{16} - 72 q^{19} - 18 q^{21} - 180 q^{24} - 78 q^{26} + 32 q^{29} + 78 q^{31} + 348 q^{36} + 204 q^{39} + 60 q^{44} - 160 q^{46} + 364 q^{49} - 210 q^{51} - 366 q^{54} - 190 q^{56} - 558 q^{59} - 282 q^{61} - 8 q^{64} + 420 q^{66} - 308 q^{71} + 538 q^{74} + 122 q^{79} - 166 q^{81} + 1506 q^{84} + 200 q^{86} - 924 q^{89} - 474 q^{91} - 1506 q^{94} + 1170 q^{96} - 508 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(175, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.3.j.a $20$ $4.768$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{13}q^{2}+(-\beta _{12}+\beta _{15})q^{3}+(-2\beta _{4}+\cdots)q^{4}+\cdots\)
175.3.j.b $24$ $4.768$ None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{3}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(175, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)