Properties

Label 1045.6.bs
Level $1045$
Weight $6$
Character orbit 1045.bs
Rep. character $\chi_{1045}(172,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $4320$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.bs (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 4832 4320 512
Cusp forms 4768 4320 448
Eisenstein series 64 0 64

Trace form

\( 4320 q - 4 q^{3} - 44 q^{5} + 590 q^{7} + O(q^{10}) \) \( 4320 q - 4 q^{3} - 44 q^{5} + 590 q^{7} - 760 q^{11} + 2144 q^{12} + 6200 q^{15} + 278000 q^{16} - 1910 q^{17} + 7424 q^{20} + 8432 q^{22} - 29120 q^{23} + 2168 q^{25} + 10160 q^{26} + 6716 q^{27} + 36480 q^{28} - 13680 q^{30} + 19360 q^{31} - 50984 q^{33} + 1419920 q^{36} - 9204 q^{37} + 104544 q^{42} - 112752 q^{45} - 438800 q^{46} - 152784 q^{47} - 141824 q^{48} + 599600 q^{51} - 392080 q^{52} + 75600 q^{53} + 27460 q^{55} + 555600 q^{56} + 80256 q^{58} - 518296 q^{60} - 227600 q^{61} - 675300 q^{62} - 238950 q^{63} - 375080 q^{66} - 517840 q^{67} + 122240 q^{68} + 440960 q^{70} + 41240 q^{71} + 899700 q^{72} - 98520 q^{73} + 254704 q^{75} - 314606 q^{77} + 207680 q^{78} + 608520 q^{80} + 6513320 q^{81} - 761680 q^{82} + 676400 q^{86} - 1288268 q^{88} - 432840 q^{91} + 741176 q^{92} - 457764 q^{93} - 364610 q^{95} - 4343400 q^{96} - 1665908 q^{97} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)