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Properties

Label 600.4.bc
Level $600$
Weight $4$
Character orbit 600.bc
Rep. character $\chi_{600}(169,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $184$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 600.bc (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(600, [\chi])\).

Total New Old
Modular forms 1472 184 1288
Cusp forms 1408 184 1224
Eisenstein series 64 0 64

Trace form

\( 184 q - 8 q^{5} + 414 q^{9} + O(q^{10}) \) \( 184 q - 8 q^{5} + 414 q^{9} - 42 q^{15} - 228 q^{19} - 84 q^{21} - 420 q^{23} + 234 q^{25} + 296 q^{29} - 414 q^{31} - 596 q^{35} + 40 q^{37} - 584 q^{41} + 72 q^{45} - 1720 q^{47} - 9972 q^{49} - 2448 q^{51} + 480 q^{53} - 2528 q^{55} + 984 q^{59} - 1796 q^{61} + 1004 q^{65} + 552 q^{69} - 696 q^{71} + 2280 q^{73} + 312 q^{75} - 84 q^{79} - 3726 q^{81} - 10380 q^{83} - 4572 q^{85} - 3420 q^{87} - 2604 q^{89} + 2328 q^{91} + 5320 q^{95} + 2790 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(600, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(600, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(600, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)