Properties

Label 605.6.m
Level $605$
Weight $6$
Character orbit 605.m
Rep. character $\chi_{605}(112,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2096$
Sturm bound $396$

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Defining parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 605.m (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(396\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(605, [\chi])\).

Total New Old
Modular forms 2736 2224 512
Cusp forms 2544 2096 448
Eisenstein series 192 128 64

Trace form

\( 2096 q + 10 q^{2} + 2 q^{3} - 38 q^{5} + 20 q^{6} + 600 q^{7} + 10 q^{8} + O(q^{10}) \) \( 2096 q + 10 q^{2} + 2 q^{3} - 38 q^{5} + 20 q^{6} + 600 q^{7} + 10 q^{8} + 1596 q^{12} + 10 q^{13} + 5018 q^{15} + 123388 q^{16} - 1900 q^{17} + 10 q^{18} + 1296 q^{20} - 29184 q^{23} + 9830 q^{25} + 8412 q^{26} + 7694 q^{27} + 18250 q^{28} - 6830 q^{30} + 9692 q^{31} + 10 q^{35} + 632028 q^{36} + 11614 q^{37} + 86250 q^{38} + 10250 q^{40} - 72280 q^{41} + 38470 q^{42} - 104188 q^{45} - 219380 q^{46} - 84820 q^{47} - 41286 q^{48} + 14250 q^{50} + 299820 q^{51} - 28350 q^{52} + 53144 q^{53} + 423304 q^{56} + 359570 q^{57} - 229894 q^{58} - 452102 q^{60} - 113780 q^{61} - 496200 q^{62} - 241370 q^{63} - 746352 q^{67} + 121930 q^{68} + 169754 q^{70} - 115388 q^{71} + 527620 q^{72} - 49250 q^{73} - 101162 q^{75} + 1377844 q^{78} + 520322 q^{80} + 2214148 q^{81} - 245706 q^{82} - 316090 q^{83} + 274770 q^{85} + 856812 q^{86} + 1102820 q^{90} - 371668 q^{91} + 534160 q^{92} - 84334 q^{93} - 701360 q^{95} - 2818080 q^{96} - 959306 q^{97} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(605, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(605, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(605, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)