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Properties

Label 1045.6.ce
Level $1045$
Weight $6$
Character orbit 1045.ce
Rep. character $\chi_{1045}(16,\cdot)$
Character field $\Q(\zeta_{45})$
Dimension $9600$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.ce (of order \(45\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 209 \)
Character field: \(\Q(\zeta_{45})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1045, [\chi])\).

Total New Old
Modular forms 14496 9600 4896
Cusp forms 14304 9600 4704
Eisenstein series 192 0 192

Trace form

\( 9600 q - 132 q^{3} - 72 q^{6} + 2304 q^{8} - 396 q^{9} + O(q^{10}) \) \( 9600 q - 132 q^{3} - 72 q^{6} + 2304 q^{8} - 396 q^{9} - 7920 q^{14} + 9756 q^{17} - 23328 q^{18} + 4224 q^{22} - 3456 q^{24} + 5280 q^{26} - 31548 q^{27} - 52938 q^{29} - 34800 q^{30} + 13092 q^{31} - 99306 q^{33} - 111624 q^{34} + 8700 q^{35} - 120504 q^{36} - 7248 q^{37} + 48096 q^{38} - 186954 q^{41} - 268626 q^{42} + 711630 q^{44} + 236256 q^{47} + 710490 q^{48} + 2833944 q^{49} + 30000 q^{50} + 421104 q^{51} + 248574 q^{52} + 157608 q^{53} - 334308 q^{54} + 101376 q^{56} - 470316 q^{57} - 257664 q^{58} - 207570 q^{59} - 113112 q^{61} - 450204 q^{62} + 4915200 q^{64} - 621300 q^{65} + 552216 q^{66} + 126324 q^{67} + 337344 q^{68} + 59796 q^{69} + 59400 q^{70} + 20508 q^{71} - 1110528 q^{72} - 965304 q^{73} + 170160 q^{74} + 978744 q^{76} - 820656 q^{77} + 202080 q^{78} - 746328 q^{81} - 501336 q^{82} + 489240 q^{84} + 82608 q^{86} + 398928 q^{88} - 656892 q^{89} - 427200 q^{90} + 370242 q^{91} + 298512 q^{93} - 824400 q^{94} + 1414560 q^{96} + 1282998 q^{97} + 1563144 q^{98} - 801438 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(1045, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(1045, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)