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Properties

Label 605.6.b
Level $605$
Weight $6$
Character orbit 605.b
Rep. character $\chi_{605}(364,\cdot)$
Character field $\Q$
Dimension $264$
Sturm bound $396$

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Defining parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 605.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Sturm bound: \(396\)

Dimensions

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

Total New Old
Modular forms 342 282 60
Cusp forms 318 264 54
Eisenstein series 24 18 6

Trace form

\( 264 q - 4084 q^{4} - 8 q^{5} - 4 q^{6} - 20324 q^{9} + O(q^{10}) \) \( 264 q - 4084 q^{4} - 8 q^{5} - 4 q^{6} - 20324 q^{9} - 430 q^{10} + 308 q^{14} - 1918 q^{15} + 62620 q^{16} + 520 q^{19} + 1356 q^{20} - 7852 q^{21} + 7112 q^{24} + 3332 q^{25} + 9120 q^{26} - 5184 q^{29} - 19834 q^{30} + 13928 q^{31} + 15128 q^{34} + 18342 q^{35} + 275008 q^{36} + 7696 q^{39} - 17668 q^{40} - 3600 q^{41} + 5014 q^{45} - 8524 q^{46} - 554380 q^{49} + 40918 q^{50} - 39780 q^{51} - 36732 q^{54} - 40496 q^{56} - 1040 q^{59} + 161920 q^{60} - 127824 q^{61} - 984828 q^{64} + 76880 q^{65} - 145972 q^{69} + 108412 q^{70} + 115256 q^{71} + 239452 q^{74} + 2826 q^{75} - 131240 q^{76} - 5364 q^{79} + 193224 q^{80} + 1082448 q^{81} + 636792 q^{84} - 185102 q^{85} - 73804 q^{86} + 133024 q^{89} + 169768 q^{90} + 209256 q^{91} + 470296 q^{94} - 240132 q^{95} - 614888 q^{96} + O(q^{100}) \)

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.

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

\( S_{6}^{\mathrm{old}}(605, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)