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Properties

Label 1805.4.l
Level $1805$
Weight $4$
Character orbit 1805.l
Rep. character $\chi_{1805}(293,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1976$
Sturm bound $760$

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Defining parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1805.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(760\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1805, [\chi])\).

Total New Old
Modular forms 2360 2104 256
Cusp forms 2200 1976 224
Eisenstein series 160 128 32

Trace form

\( 1976 q + 6 q^{2} + 6 q^{3} - 14 q^{5} + 16 q^{6} + 24 q^{7} + O(q^{10}) \) \( 1976 q + 6 q^{2} + 6 q^{3} - 14 q^{5} + 16 q^{6} + 24 q^{7} + 6 q^{10} + 72 q^{11} + 6 q^{13} - 246 q^{15} + 14240 q^{16} - 78 q^{17} + 952 q^{20} + 300 q^{21} + 486 q^{22} + 82 q^{23} - 294 q^{25} + 496 q^{26} - 604 q^{28} - 588 q^{30} - 1128 q^{32} + 1356 q^{33} + 526 q^{35} - 29308 q^{36} + 1092 q^{40} - 1320 q^{41} - 1146 q^{42} + 1514 q^{43} - 1364 q^{45} - 274 q^{47} - 3972 q^{48} + 1116 q^{51} + 54 q^{52} + 942 q^{53} + 1004 q^{55} - 6212 q^{58} + 4326 q^{60} + 964 q^{61} - 1068 q^{62} - 1216 q^{63} + 2372 q^{66} - 1242 q^{67} + 4276 q^{68} - 3018 q^{70} + 12 q^{71} + 13548 q^{72} - 2734 q^{73} + 9800 q^{77} + 6192 q^{78} + 2978 q^{80} + 60272 q^{81} + 2980 q^{82} + 6344 q^{83} + 1034 q^{85} + 7800 q^{86} - 11572 q^{87} - 8712 q^{90} - 9132 q^{91} - 6428 q^{92} - 2592 q^{93} - 35504 q^{96} - 3306 q^{97} - 10500 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1805, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1805, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1805, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)