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Properties

Label 950.6.bi
Level $950$
Weight $6$
Character orbit 950.bi
Rep. character $\chi_{950}(3,\cdot)$
Character field $\Q(\zeta_{180})$
Dimension $12000$
Sturm bound $900$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 950.bi (of order \(180\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{180})\)
Sturm bound: \(900\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(950, [\chi])\).

Total New Old
Modular forms 36192 12000 24192
Cusp forms 35808 12000 23808
Eisenstein series 384 0 384

Trace form

\( 12000 q - 708 q^{7} + O(q^{10}) \) \( 12000 q - 708 q^{7} + 6516 q^{15} + 3204 q^{17} + 22656 q^{22} + 28440 q^{23} - 7656 q^{25} + 85080 q^{29} + 18216 q^{33} + 25884 q^{35} + 308952 q^{43} + 11916 q^{45} - 159456 q^{47} - 230976 q^{50} - 95436 q^{53} + 259272 q^{55} - 542604 q^{57} + 506280 q^{59} + 84864 q^{60} - 95136 q^{62} - 43236 q^{63} + 3606480 q^{65} - 72864 q^{67} + 36672 q^{68} + 103488 q^{70} - 210564 q^{73} - 424080 q^{77} - 512256 q^{78} + 382272 q^{82} - 107124 q^{83} + 4397760 q^{84} + 2385312 q^{85} + 1161408 q^{87} - 176928 q^{90} - 100992 q^{92} - 1386876 q^{93} - 1148664 q^{95} + 43320 q^{97} - 472224 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(950, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(950, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)