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Properties

Label 950.6.f
Level $950$
Weight $6$
Character orbit 950.f
Rep. character $\chi_{950}(493,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $300$
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.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(i)\)
Sturm bound: \(900\)

Dimensions

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

Total New Old
Modular forms 1524 300 1224
Cusp forms 1476 300 1176
Eisenstein series 48 0 48

Trace form

\( 300 q + 236 q^{7} + O(q^{10}) \) \( 300 q + 236 q^{7} - 80 q^{11} - 76800 q^{16} - 2900 q^{17} + 16644 q^{23} - 3520 q^{26} + 3776 q^{28} + 388800 q^{36} - 15376 q^{38} + 40832 q^{42} - 105124 q^{43} - 95180 q^{47} - 64112 q^{57} - 21680 q^{61} + 63424 q^{62} - 152212 q^{63} + 127840 q^{66} - 46400 q^{68} + 337548 q^{73} - 89600 q^{76} - 206744 q^{77} - 1901100 q^{81} + 127424 q^{82} + 387020 q^{83} - 401432 q^{87} - 266304 q^{92} - 681064 q^{93} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)