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Properties

Label 175.5.w
Level $175$
Weight $5$
Character orbit 175.w
Rep. character $\chi_{175}(2,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1248$
Sturm bound $100$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 175.w (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(100\)

Dimensions

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

Total New Old
Modular forms 1312 1312 0
Cusp forms 1248 1248 0
Eisenstein series 64 64 0

Trace form

\( 1248 q - 8 q^{2} - 8 q^{3} - 10 q^{4} - 26 q^{5} - 24 q^{6} - 66 q^{7} - 148 q^{8} - 10 q^{9} + O(q^{10}) \) \( 1248 q - 8 q^{2} - 8 q^{3} - 10 q^{4} - 26 q^{5} - 24 q^{6} - 66 q^{7} - 148 q^{8} - 10 q^{9} + 56 q^{10} - 6 q^{11} + 348 q^{12} - 32 q^{13} - 20 q^{14} + 28 q^{15} - 9222 q^{16} - 2138 q^{17} + 858 q^{18} - 10 q^{19} + 992 q^{20} - 12 q^{21} - 6496 q^{22} - 728 q^{23} - 1654 q^{25} - 16 q^{26} - 1268 q^{27} - 4822 q^{28} + 6560 q^{29} - 74 q^{30} - 6 q^{31} + 4156 q^{32} + 2478 q^{33} - 40 q^{34} - 3250 q^{35} - 56728 q^{36} - 538 q^{37} + 10016 q^{38} - 8810 q^{39} - 3732 q^{40} - 24 q^{41} + 6278 q^{42} + 17108 q^{43} - 10 q^{44} - 14406 q^{45} - 6 q^{46} - 4718 q^{47} + 15100 q^{48} + 4840 q^{50} - 16 q^{51} + 4856 q^{52} - 24638 q^{53} - 10 q^{54} - 24928 q^{55} + 1012 q^{56} - 54688 q^{57} - 17760 q^{58} + 7190 q^{59} - 12 q^{60} - 6 q^{61} + 8904 q^{62} + 42214 q^{63} + 87260 q^{64} + 19438 q^{65} + 5178 q^{66} + 5712 q^{67} - 67086 q^{68} + 79060 q^{69} - 3140 q^{70} - 24 q^{71} - 9138 q^{72} - 22378 q^{73} + 14040 q^{75} + 1984 q^{76} - 50928 q^{77} - 81124 q^{78} - 10 q^{79} + 12874 q^{80} - 90402 q^{81} + 4224 q^{82} - 164432 q^{83} + 55180 q^{84} + 71016 q^{85} - 6 q^{86} - 35040 q^{87} + 47006 q^{88} - 35260 q^{89} + 352820 q^{90} - 12 q^{91} + 80908 q^{92} + 76798 q^{93} - 10 q^{94} + 74978 q^{95} + 2106 q^{96} + 119408 q^{97} + 23826 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

The newforms in this space have not yet been added to the LMFDB.