Properties

Label 175.2.h
Level $175$
Weight $2$
Character orbit 175.h
Rep. character $\chi_{175}(36,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $64$
Newform subspaces $3$
Sturm bound $40$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 3 \)
Sturm bound: \(40\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 88 64 24
Cusp forms 72 64 8
Eisenstein series 16 0 16

Trace form

\( 64 q - 2 q^{2} - 4 q^{3} - 18 q^{4} + 4 q^{5} - 6 q^{8} - 24 q^{9} + O(q^{10}) \) \( 64 q - 2 q^{2} - 4 q^{3} - 18 q^{4} + 4 q^{5} - 6 q^{8} - 24 q^{9} - 14 q^{10} - 8 q^{11} + 8 q^{12} - 24 q^{13} - 4 q^{14} + 2 q^{15} + 2 q^{16} - 16 q^{17} + 4 q^{18} + 12 q^{19} + 8 q^{20} - 4 q^{21} + 26 q^{22} - 6 q^{23} - 28 q^{24} + 22 q^{25} - 32 q^{26} + 2 q^{27} - 22 q^{29} - 32 q^{30} - 12 q^{31} + 16 q^{32} - 16 q^{33} + 30 q^{34} - 2 q^{35} - 16 q^{36} + 28 q^{37} - 10 q^{38} - 4 q^{39} + 64 q^{40} - 24 q^{41} + 30 q^{42} - 44 q^{43} + 22 q^{44} - 10 q^{45} + 4 q^{46} + 38 q^{47} + 78 q^{48} + 64 q^{49} - 4 q^{50} + 44 q^{51} - 92 q^{52} - 34 q^{53} + 54 q^{54} + 6 q^{55} - 12 q^{56} - 68 q^{57} + 66 q^{58} - 6 q^{59} + 12 q^{60} - 16 q^{61} - 46 q^{62} + 12 q^{63} - 6 q^{64} + 60 q^{65} + 74 q^{66} + 2 q^{67} - 116 q^{68} - 18 q^{69} - 16 q^{70} - 32 q^{71} - 50 q^{72} - 28 q^{73} + 40 q^{74} - 100 q^{75} - 52 q^{76} + 12 q^{77} + 142 q^{78} - 14 q^{80} + 2 q^{81} - 28 q^{82} - 74 q^{83} - 12 q^{84} + 38 q^{85} + 20 q^{86} + 82 q^{87} - 44 q^{88} + 28 q^{89} - 202 q^{90} - 8 q^{91} + 8 q^{92} + 16 q^{93} + 48 q^{94} + 58 q^{95} - 12 q^{96} - 58 q^{97} - 2 q^{98} + 20 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.2.h.a 175.h 25.d $4$ $1.397$ \(\Q(\zeta_{10})\) None \(-5\) \(-4\) \(-5\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
175.2.h.b 175.h 25.d $28$ $1.397$ None \(6\) \(4\) \(8\) \(-28\) $\mathrm{SU}(2)[C_{5}]$
175.2.h.c 175.h 25.d $32$ $1.397$ None \(-3\) \(-4\) \(1\) \(32\) $\mathrm{SU}(2)[C_{5}]$

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

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