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Properties

Label 1045.6.bh
Level $1045$
Weight $6$
Character orbit 1045.bh
Rep. character $\chi_{1045}(26,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $3200$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.bh (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 209 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 4832 3200 1632
Cusp forms 4768 3200 1568
Eisenstein series 64 0 64

Trace form

\( 3200 q + 16 q^{2} + 44 q^{3} + 6400 q^{4} + 24 q^{6} - 1536 q^{8} + 32532 q^{9} + O(q^{10}) \) \( 3200 q + 16 q^{2} + 44 q^{3} + 6400 q^{4} + 24 q^{6} - 1536 q^{8} + 32532 q^{9} - 1600 q^{10} + 936 q^{11} - 4224 q^{12} + 1352 q^{13} - 616 q^{14} + 102400 q^{16} - 9276 q^{17} - 19344 q^{18} - 4262 q^{19} + 4280 q^{22} - 8608 q^{23} + 9232 q^{24} + 250000 q^{25} - 768 q^{26} + 5588 q^{27} - 5070 q^{29} + 23200 q^{30} + 17456 q^{31} - 77528 q^{32} + 52954 q^{33} - 12556 q^{34} - 2900 q^{35} + 525508 q^{36} + 4832 q^{37} + 1698 q^{38} + 65196 q^{39} + 19200 q^{40} + 62318 q^{41} + 135202 q^{42} - 25224 q^{43} + 72968 q^{44} + 150496 q^{46} + 39376 q^{47} - 94326 q^{48} - 1972964 q^{49} - 20000 q^{50} + 58154 q^{51} - 17962 q^{52} - 52536 q^{53} + 246956 q^{54} + 473696 q^{56} - 310446 q^{57} + 106944 q^{58} + 8690 q^{59} + 12528 q^{61} - 260100 q^{62} - 5240 q^{63} - 3557960 q^{64} + 794000 q^{65} + 186104 q^{66} - 42108 q^{67} + 761984 q^{68} + 107772 q^{69} + 9900 q^{70} - 6836 q^{71} - 553832 q^{72} - 50700 q^{73} + 113100 q^{74} + 82500 q^{75} - 1898432 q^{76} + 1209732 q^{77} - 554440 q^{78} - 150804 q^{79} - 72600 q^{80} + 2728834 q^{81} - 152000 q^{82} - 396936 q^{83} + 38872 q^{84} + 80704 q^{86} + 1499360 q^{87} + 1133084 q^{88} + 1068120 q^{89} + 304400 q^{90} - 123414 q^{91} - 17144 q^{92} - 272160 q^{93} - 500016 q^{94} + 1434984 q^{96} - 350154 q^{97} - 1122452 q^{98} + 812508 q^{99} + O(q^{100}) \)

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

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