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Properties

Label 245.6.s
Level $245$
Weight $6$
Character orbit 245.s
Rep. character $\chi_{245}(13,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $1656$
Sturm bound $168$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 245.s (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(168\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(245, [\chi])\).

Total New Old
Modular forms 1704 1704 0
Cusp forms 1656 1656 0
Eisenstein series 48 48 0

Trace form

\( 1656 q - 10 q^{2} - 14 q^{3} - 14 q^{5} + 532 q^{6} + 182 q^{7} + 354 q^{8} + O(q^{10}) \) \( 1656 q - 10 q^{2} - 14 q^{3} - 14 q^{5} + 532 q^{6} + 182 q^{7} + 354 q^{8} - 14 q^{10} - 60 q^{11} - 14 q^{12} - 14 q^{13} - 202 q^{15} + 69084 q^{16} - 2688 q^{17} - 1124 q^{18} - 14 q^{20} + 56 q^{21} + 7238 q^{22} + 5094 q^{23} + 4434 q^{25} - 6188 q^{26} - 14 q^{27} - 21294 q^{28} - 19340 q^{30} - 43338 q^{32} - 14 q^{33} + 34846 q^{35} + 414764 q^{36} + 5402 q^{37} - 462 q^{38} - 14 q^{40} - 54488 q^{41} + 84238 q^{42} + 58394 q^{43} - 13566 q^{45} + 118620 q^{46} - 96572 q^{47} + 456464 q^{50} + 52180 q^{51} - 14 q^{52} - 175460 q^{53} + 158704 q^{55} - 139860 q^{56} + 25398 q^{57} - 30826 q^{58} - 211970 q^{60} + 75852 q^{61} + 434 q^{62} - 88046 q^{63} + 89402 q^{65} - 577248 q^{66} + 207664 q^{67} + 538538 q^{70} + 378740 q^{71} - 648996 q^{72} - 14 q^{73} - 4970 q^{75} - 28700 q^{76} - 219730 q^{77} + 328942 q^{78} + 2200884 q^{81} - 880474 q^{82} + 462504 q^{83} - 193674 q^{85} + 120740 q^{86} + 783454 q^{87} - 515148 q^{88} + 379330 q^{90} - 766444 q^{91} - 146102 q^{92} + 1268170 q^{93} - 455496 q^{95} + 628712 q^{96} + 2830296 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(245, [\chi])\) into newform subspaces

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