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Properties

Label 605.6.k
Level $605$
Weight $6$
Character orbit 605.k
Rep. character $\chi_{605}(56,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $2200$
Sturm bound $396$

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Defining parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 605.k (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(396\)

Dimensions

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

Total New Old
Modular forms 3320 2200 1120
Cusp forms 3280 2200 1080
Eisenstein series 40 0 40

Trace form

\( 2200 q - 4 q^{2} + 44 q^{3} - 3476 q^{4} - 16 q^{6} - 196 q^{7} - 612 q^{8} + 178112 q^{9} + O(q^{10}) \) \( 2200 q - 4 q^{2} + 44 q^{3} - 3476 q^{4} - 16 q^{6} - 196 q^{7} - 612 q^{8} + 178112 q^{9} - 200 q^{10} + 148 q^{11} - 9504 q^{12} - 2494 q^{13} + 308 q^{14} - 4950 q^{15} - 59092 q^{16} + 4312 q^{17} - 6164 q^{18} - 208 q^{19} + 1408 q^{21} + 1264 q^{22} + 9460 q^{23} + 35376 q^{24} - 137500 q^{25} + 13376 q^{26} + 440 q^{27} + 28932 q^{28} - 6184 q^{29} + 8000 q^{30} + 26488 q^{31} - 56408 q^{32} + 3764 q^{33} + 45276 q^{34} - 12700 q^{35} - 250932 q^{36} + 27544 q^{37} - 7788 q^{38} + 26392 q^{39} + 96000 q^{40} + 41064 q^{41} - 13596 q^{42} - 17684 q^{43} + 178434 q^{44} - 59288 q^{46} + 28468 q^{47} + 73524 q^{48} - 443652 q^{49} - 2500 q^{50} - 221426 q^{51} - 186744 q^{52} + 314600 q^{53} + 488966 q^{54} + 15800 q^{55} - 139898 q^{56} - 636974 q^{57} + 448954 q^{58} - 1804 q^{59} + 78100 q^{60} + 73928 q^{61} - 264742 q^{62} - 187156 q^{63} - 333300 q^{64} - 14400 q^{65} + 322084 q^{66} + 74734 q^{67} + 48764 q^{68} - 93720 q^{69} - 6600 q^{70} - 65428 q^{71} - 209556 q^{72} - 283684 q^{73} + 52840 q^{74} + 27500 q^{75} + 124320 q^{76} - 241700 q^{77} + 941688 q^{78} - 710220 q^{79} - 48400 q^{80} + 14327720 q^{81} - 1024056 q^{82} - 362292 q^{83} + 492848 q^{84} + 50750 q^{85} + 148104 q^{86} - 38328 q^{87} + 223712 q^{88} - 719928 q^{89} - 721800 q^{90} - 907236 q^{91} - 202708 q^{92} + 1193830 q^{93} - 171440 q^{94} - 144400 q^{95} + 770424 q^{96} - 243958 q^{97} - 2137964 q^{98} - 33596 q^{99} + O(q^{100}) \)

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.

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

\( S_{6}^{\mathrm{old}}(605, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)