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Properties

Label 175.5.u
Level $175$
Weight $5$
Character orbit 175.u
Rep. character $\chi_{175}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $624$
Sturm bound $100$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 175.u (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(100\)

Dimensions

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

Total New Old
Modular forms 656 656 0
Cusp forms 624 624 0
Eisenstein series 32 32 0

Trace form

\( 624 q - 5 q^{2} - 15 q^{3} - 611 q^{4} + 15 q^{5} - 470 q^{8} + 1995 q^{9} + O(q^{10}) \) \( 624 q - 5 q^{2} - 15 q^{3} - 611 q^{4} + 15 q^{5} - 470 q^{8} + 1995 q^{9} - 405 q^{10} + 42 q^{11} - 15 q^{12} - 144 q^{14} - 2160 q^{15} + 4573 q^{16} - 15 q^{17} - 9 q^{19} + 747 q^{21} + 3180 q^{22} + 1945 q^{23} - 2046 q^{24} - 45 q^{25} + 72 q^{26} - 6090 q^{28} - 1992 q^{29} - 1625 q^{30} - 6849 q^{31} + 4860 q^{33} + 8540 q^{35} + 42020 q^{36} - 5 q^{37} - 22290 q^{38} - 5131 q^{39} - 6525 q^{40} - 5770 q^{42} - 99 q^{44} + 27585 q^{45} + 7721 q^{46} - 15 q^{47} - 3426 q^{49} + 24850 q^{50} - 92 q^{51} - 38490 q^{52} - 16055 q^{53} - 7689 q^{54} + 19590 q^{56} + 6895 q^{58} - 6489 q^{59} + 14885 q^{60} + 9261 q^{61} - 3265 q^{63} + 62934 q^{64} - 5295 q^{65} - 23631 q^{66} + 3595 q^{67} - 30085 q^{70} + 13038 q^{71} - 33750 q^{72} - 62415 q^{73} - 21154 q^{74} - 59205 q^{75} + 5385 q^{77} - 830 q^{78} - 13303 q^{79} + 81090 q^{80} + 33997 q^{81} - 42359 q^{84} + 59410 q^{85} + 24585 q^{86} - 15 q^{87} - 27680 q^{88} + 31716 q^{89} - 23162 q^{91} + 75130 q^{92} + 42231 q^{94} + 17875 q^{95} - 76815 q^{96} + 56170 q^{98} + 9180 q^{99} + O(q^{100}) \)

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.