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Properties

Label 175.5.l
Level $175$
Weight $5$
Character orbit 175.l
Rep. character $\chi_{175}(6,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $312$
Sturm bound $100$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 175.l (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(100\)

Dimensions

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

Total New Old
Modular forms 328 328 0
Cusp forms 312 312 0
Eisenstein series 16 16 0

Trace form

\( 312 q - 6 q^{2} - 614 q^{4} - 58 q^{7} - 212 q^{8} + 1992 q^{9} + O(q^{10}) \) \( 312 q - 6 q^{2} - 614 q^{4} - 58 q^{7} - 212 q^{8} + 1992 q^{9} - 96 q^{11} + 39 q^{14} + 980 q^{15} - 4550 q^{16} - 916 q^{18} + 750 q^{21} - 262 q^{22} - 2136 q^{23} + 240 q^{25} + 3571 q^{28} - 996 q^{29} + 7750 q^{30} + 7252 q^{32} + 465 q^{35} + 8236 q^{36} - 2986 q^{37} - 2990 q^{39} + 8095 q^{42} + 20704 q^{43} + 3002 q^{44} - 12382 q^{46} + 3402 q^{49} - 10920 q^{50} - 820 q^{51} + 12144 q^{53} - 992 q^{56} - 51120 q^{57} + 22918 q^{58} - 6140 q^{60} - 4138 q^{63} + 6704 q^{64} + 740 q^{65} + 6994 q^{67} + 41760 q^{70} + 27084 q^{71} + 24798 q^{72} - 19332 q^{74} - 36126 q^{77} - 19300 q^{78} - 14546 q^{79} - 89768 q^{81} - 12840 q^{84} - 12890 q^{85} - 1482 q^{86} + 13536 q^{88} + 10060 q^{91} + 26972 q^{92} - 37040 q^{93} + 47660 q^{95} - 20151 q^{98} + 31644 q^{99} + O(q^{100}) \)

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.