Properties

Label 175.2.h
Level 175
Weight 2
Character orbit 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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
175.2.h.a \(4\) \(1.397\) \(\Q(\zeta_{10})\) None \(-5\) \(-4\) \(-5\) \(-4\) \(q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
175.2.h.b \(28\) \(1.397\) None \(6\) \(4\) \(8\) \(-28\)
175.2.h.c \(32\) \(1.397\) None \(-3\) \(-4\) \(1\) \(32\)

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

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

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 5 T + 13 T^{2} + 25 T^{3} + 39 T^{4} + 50 T^{5} + 52 T^{6} + 40 T^{7} + 16 T^{8} \))
$3$ (\( 1 + 4 T + 13 T^{2} + 30 T^{3} + 61 T^{4} + 90 T^{5} + 117 T^{6} + 108 T^{7} + 81 T^{8} \))
$5$ (\( 1 + 5 T + 15 T^{2} + 25 T^{3} + 25 T^{4} \))
$7$ (\( ( 1 + T )^{4} \))
$11$ (\( 1 + 2 T - 7 T^{2} - 36 T^{3} + 5 T^{4} - 396 T^{5} - 847 T^{6} + 2662 T^{7} + 14641 T^{8} \))
$13$ (\( 1 - 3 T^{2} + 40 T^{3} + 129 T^{4} + 520 T^{5} - 507 T^{6} + 28561 T^{8} \))
$17$ (\( 1 + 12 T + 77 T^{2} + 420 T^{3} + 1981 T^{4} + 7140 T^{5} + 22253 T^{6} + 58956 T^{7} + 83521 T^{8} \))
$19$ (\( 1 + 2 T - 15 T^{2} - 68 T^{3} + 149 T^{4} - 1292 T^{5} - 5415 T^{6} + 13718 T^{7} + 130321 T^{8} \))
$23$ (\( 1 + 16 T + 113 T^{2} + 570 T^{3} + 2741 T^{4} + 13110 T^{5} + 59777 T^{6} + 194672 T^{7} + 279841 T^{8} \))
$29$ (\( 1 - 2 T - 25 T^{2} - 32 T^{3} + 929 T^{4} - 928 T^{5} - 21025 T^{6} - 48778 T^{7} + 707281 T^{8} \))
$31$ (\( 1 + 16 T + 105 T^{2} + 554 T^{3} + 3269 T^{4} + 17174 T^{5} + 100905 T^{6} + 476656 T^{7} + 923521 T^{8} \))
$37$ (\( 1 + 3 T - 33 T^{2} - 35 T^{3} + 1296 T^{4} - 1295 T^{5} - 45177 T^{6} + 151959 T^{7} + 1874161 T^{8} \))
$41$ (\( 1 + 8 T - 7 T^{2} + 36 T^{3} + 1925 T^{4} + 1476 T^{5} - 11767 T^{6} + 551368 T^{7} + 2825761 T^{8} \))
$43$ (\( ( 1 + 10 T + 106 T^{2} + 430 T^{3} + 1849 T^{4} )^{2} \))
$47$ (\( 1 + 16 T + 49 T^{2} - 628 T^{3} - 7311 T^{4} - 29516 T^{5} + 108241 T^{6} + 1661168 T^{7} + 4879681 T^{8} \))
$53$ (\( 1 - 17 T + 71 T^{2} + 849 T^{3} - 12256 T^{4} + 44997 T^{5} + 199439 T^{6} - 2530909 T^{7} + 7890481 T^{8} \))
$59$ (\( 1 - 19 T^{2} - 390 T^{3} + 2701 T^{4} - 23010 T^{5} - 66139 T^{6} + 12117361 T^{8} \))
$61$ (\( 1 + 8 T - 27 T^{2} - 584 T^{3} - 2575 T^{4} - 35624 T^{5} - 100467 T^{6} + 1815848 T^{7} + 13845841 T^{8} \))
$67$ (\( 1 - 6 T + 69 T^{2} - 382 T^{3} + 1329 T^{4} - 25594 T^{5} + 309741 T^{6} - 1804578 T^{7} + 20151121 T^{8} \))
$71$ (\( 1 + 20 T + 169 T^{2} + 1600 T^{3} + 17121 T^{4} + 113600 T^{5} + 851929 T^{6} + 7158220 T^{7} + 25411681 T^{8} \))
$73$ (\( 1 - 12 T + 21 T^{2} - 476 T^{3} + 9429 T^{4} - 34748 T^{5} + 111909 T^{6} - 4668204 T^{7} + 28398241 T^{8} \))
$79$ (\( 1 - 6 T + 57 T^{2} - 118 T^{3} + 105 T^{4} - 9322 T^{5} + 355737 T^{6} - 2958234 T^{7} + 38950081 T^{8} \))
$83$ (\( 1 - 12 T - 19 T^{2} + 204 T^{3} + 4489 T^{4} + 16932 T^{5} - 130891 T^{6} - 6861444 T^{7} + 47458321 T^{8} \))
$89$ (\( 1 + 3 T - 35 T^{2} + 693 T^{3} + 9604 T^{4} + 61677 T^{5} - 277235 T^{6} + 2114907 T^{7} + 62742241 T^{8} \))
$97$ (\( 1 + 36 T + 549 T^{2} + 5092 T^{3} + 43869 T^{4} + 493924 T^{5} + 5165541 T^{6} + 32856228 T^{7} + 88529281 T^{8} \))
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