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Properties

Label 175.4.k
Level $175$
Weight $4$
Character orbit 175.k
Rep. character $\chi_{175}(74,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $68$
Newform subspaces $5$
Sturm bound $80$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 175.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(80\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 132 76 56
Cusp forms 108 68 40
Eisenstein series 24 8 16

Trace form

\( 68 q + 130 q^{4} + 88 q^{6} + 212 q^{9} + O(q^{10}) \) \( 68 q + 130 q^{4} + 88 q^{6} + 212 q^{9} - 50 q^{11} - 38 q^{14} - 522 q^{16} + 50 q^{19} + 598 q^{21} + 536 q^{24} - 546 q^{26} - 496 q^{29} - 666 q^{31} + 472 q^{34} + 860 q^{36} - 528 q^{39} + 1304 q^{41} + 60 q^{44} + 548 q^{46} + 300 q^{49} - 1498 q^{51} + 4042 q^{54} + 1830 q^{56} + 3282 q^{59} - 1050 q^{61} - 10360 q^{64} - 2472 q^{66} - 5484 q^{69} + 3280 q^{71} - 3194 q^{74} - 5116 q^{76} - 2366 q^{79} - 1530 q^{81} + 12686 q^{84} + 3072 q^{86} + 8254 q^{89} - 940 q^{91} + 4930 q^{94} - 1846 q^{96} - 20248 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.4.k.a 175.k 35.j $4$ $10.325$ \(\Q(\zeta_{12})\) None 7.4.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\zeta_{12}q^{2}+(7\zeta_{12}-7\zeta_{12}^{3})q^{3}-4\zeta_{12}^{2}q^{4}+\cdots\)
175.4.k.b 175.k 35.j $4$ $10.325$ \(\Q(\zeta_{12})\) None 35.4.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+3\zeta_{12}q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\)
175.4.k.c 175.k 35.j $8$ $10.325$ \(\Q(\zeta_{24})\) None 35.4.e.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}^{3}+2\zeta_{24}^{7})q^{2}+(-2\zeta_{24}^{2}+\cdots)q^{3}+\cdots\)
175.4.k.d 175.k 35.j $20$ $10.325$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 35.4.e.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{14})q^{2}+(\beta _{6}+\beta _{8})q^{3}+(7-7\beta _{7}+\cdots)q^{4}+\cdots\)
175.4.k.e 175.k 35.j $32$ $10.325$ None 175.4.e.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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