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Properties

Label 605.6.o
Level $605$
Weight $6$
Character orbit 605.o
Rep. character $\chi_{605}(34,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $3280$
Sturm bound $396$

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Defining parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 605.o (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(396\)

Dimensions

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

Total New Old
Modular forms 3320 3320 0
Cusp forms 3280 3280 0
Eisenstein series 40 40 0

Trace form

\( 3280 q + 5198 q^{4} + 13 q^{5} + 414 q^{6} - 262700 q^{9} + O(q^{10}) \) \( 3280 q + 5198 q^{4} + 13 q^{5} + 414 q^{6} - 262700 q^{9} + 2727 q^{10} - 1780 q^{11} + 734 q^{14} + 2178 q^{15} - 77474 q^{16} + 938 q^{19} + 3977 q^{20} - 152 q^{21} + 51596 q^{24} - 1835 q^{25} + 12834 q^{26} + 8654 q^{29} - 5292 q^{30} - 8466 q^{31} + 1614 q^{34} + 14371 q^{35} - 437772 q^{36} + 17772 q^{39} - 8890 q^{40} - 3226 q^{41} - 10914 q^{44} + 19197 q^{45} + 23750 q^{46} + 790862 q^{49} - 131771 q^{50} + 700 q^{51} + 198734 q^{54} - 26842 q^{55} + 233282 q^{56} + 5614 q^{59} + 109758 q^{60} - 116450 q^{61} + 1150526 q^{64} - 27708 q^{65} - 26356 q^{66} + 91124 q^{69} - 51615 q^{70} - 534442 q^{71} + 424758 q^{74} + 80476 q^{75} + 841688 q^{76} - 452206 q^{79} + 908390 q^{80} + 20499008 q^{81} + 613604 q^{84} + 71363 q^{85} - 147370 q^{86} + 178292 q^{89} - 1428301 q^{90} + 277472 q^{91} - 1226476 q^{94} + 315665 q^{95} - 444828 q^{96} - 745314 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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