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Properties

Label 675.4.r
Level $675$
Weight $4$
Character orbit 675.r
Rep. character $\chi_{675}(46,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $704$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 675.r (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(675, [\chi])\).

Total New Old
Modular forms 2208 736 1472
Cusp forms 2112 704 1408
Eisenstein series 96 32 64

Trace form

\( 704 q + 3 q^{2} + 341 q^{4} + 20 q^{5} - 8 q^{7} + 44 q^{8} + O(q^{10}) \) \( 704 q + 3 q^{2} + 341 q^{4} + 20 q^{5} - 8 q^{7} + 44 q^{8} - 32 q^{10} - 85 q^{11} - 3 q^{13} - 157 q^{14} + 1325 q^{16} - 84 q^{17} - 12 q^{19} + 137 q^{20} - 35 q^{22} + 131 q^{23} + 284 q^{25} - 2432 q^{26} + 340 q^{28} - 345 q^{29} - 39 q^{31} + 372 q^{32} + 13 q^{34} - 1784 q^{35} - 156 q^{37} - 1795 q^{38} + 169 q^{40} - 653 q^{41} - 8 q^{43} + 2060 q^{44} - 44 q^{46} - 1343 q^{47} - 14904 q^{49} + 909 q^{50} - 283 q^{52} - 1788 q^{53} - 1274 q^{55} - 72 q^{56} + 469 q^{58} - 915 q^{59} - 3 q^{61} - 6088 q^{62} - 9692 q^{64} - 120 q^{65} - 921 q^{67} - 2484 q^{68} - 1762 q^{70} - 24 q^{71} - 12 q^{73} + 3798 q^{74} + 88 q^{76} - 4759 q^{77} - 255 q^{79} + 15302 q^{80} - 3808 q^{82} + 1027 q^{83} + 949 q^{85} - 4545 q^{86} + 2869 q^{88} + 524 q^{89} + 2046 q^{91} - 299 q^{92} - 2519 q^{94} + 2177 q^{95} + 1941 q^{97} - 2486 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(675, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(675, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(675, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)