Properties

Label 175.5.i
Level $175$
Weight $5$
Character orbit 175.i
Rep. character $\chi_{175}(26,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $5$
Sturm bound $100$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 175.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(100\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(175, [\chi])\).

Total New Old
Modular forms 172 108 64
Cusp forms 148 96 52
Eisenstein series 24 12 12

Trace form

\( 96 q - 2 q^{2} + 12 q^{3} - 370 q^{4} + 54 q^{7} + 68 q^{8} + 1212 q^{9} + O(q^{10}) \) \( 96 q - 2 q^{2} + 12 q^{3} - 370 q^{4} + 54 q^{7} + 68 q^{8} + 1212 q^{9} - 42 q^{11} - 678 q^{12} - 118 q^{14} - 3154 q^{16} + 1110 q^{17} + 632 q^{18} + 282 q^{19} + 1116 q^{21} - 1320 q^{22} + 952 q^{23} - 5904 q^{24} - 246 q^{26} + 162 q^{28} + 3520 q^{29} + 960 q^{31} + 174 q^{32} - 2454 q^{33} - 12396 q^{36} - 798 q^{37} - 3012 q^{38} - 24 q^{39} - 1902 q^{42} + 5220 q^{43} - 2644 q^{44} + 2360 q^{46} + 12954 q^{47} + 8044 q^{49} + 1464 q^{51} + 10668 q^{52} + 2842 q^{53} - 25254 q^{54} - 22082 q^{56} - 26316 q^{57} - 270 q^{58} - 12336 q^{59} + 3480 q^{61} + 23968 q^{63} + 85168 q^{64} + 47628 q^{66} + 1284 q^{67} - 13968 q^{68} - 14076 q^{71} + 13348 q^{72} - 27990 q^{73} - 4694 q^{74} - 31598 q^{77} - 14712 q^{78} - 26668 q^{79} - 29184 q^{81} + 38178 q^{82} - 17466 q^{84} - 17072 q^{86} + 21498 q^{87} + 39060 q^{88} - 54474 q^{89} - 7150 q^{91} - 41172 q^{92} + 15462 q^{93} - 24330 q^{94} + 63450 q^{96} + 77434 q^{98} + 31812 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(175, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.5.i.a 175.i 7.d $4$ $18.090$ \(\Q(\sqrt{-3}, \sqrt{22})\) None \(4\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2+\beta _{1}+2\beta _{2})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
175.5.i.b 175.i 7.d $20$ $18.090$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-6\) \(18\) \(0\) \(54\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{1}+\beta _{2}-\beta _{3})q^{2}+(1+\beta _{3}+\cdots)q^{3}+\cdots\)
175.5.i.c 175.i 7.d $22$ $18.090$ None \(-3\) \(9\) \(0\) \(82\) $\mathrm{SU}(2)[C_{6}]$
175.5.i.d 175.i 7.d $22$ $18.090$ None \(3\) \(-9\) \(0\) \(-82\) $\mathrm{SU}(2)[C_{6}]$
175.5.i.e 175.i 7.d $28$ $18.090$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{5}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(175, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)