↑

Properties

Label 2205.4.en
Level $2205$
Weight $4$
Character orbit 2205.en
Rep. character $\chi_{2205}(23,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $24096$
Sturm bound $1344$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2205.en (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2205 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2205, [\chi])\).

Total New Old
Modular forms 24288 24288 0
Cusp forms 24096 24096 0
Eisenstein series 192 192 0

Trace form

\( 24096 q - 42 q^{2} - 26 q^{3} - 36 q^{5} - 12 q^{7} + O(q^{10}) \) \( 24096 q - 42 q^{2} - 26 q^{3} - 36 q^{5} - 12 q^{7} - 52 q^{10} - 72 q^{11} - 258 q^{12} - 10 q^{13} - 104 q^{15} + 63468 q^{16} + 144 q^{17} + 52 q^{18} - 30 q^{20} - 424 q^{21} - 42 q^{22} - 36 q^{23} - 16 q^{25} - 32 q^{27} - 160 q^{28} + 656 q^{30} - 48 q^{31} - 42 q^{32} - 558 q^{33} + 1384 q^{36} - 52 q^{37} - 276 q^{38} - 272 q^{40} + 1176 q^{41} - 3764 q^{42} - 10 q^{43} - 5646 q^{45} - 6656 q^{46} - 42 q^{47} - 1834 q^{48} + 600 q^{50} - 52 q^{51} - 304 q^{52} - 540 q^{55} - 3240 q^{56} + 2958 q^{57} - 6536 q^{58} + 278 q^{60} - 92 q^{61} - 336 q^{62} - 2496 q^{63} - 42 q^{65} - 704 q^{66} - 24 q^{67} + 1500 q^{68} - 512 q^{70} + 2262 q^{72} - 52 q^{73} + 6050 q^{75} - 3348 q^{76} - 3300 q^{77} + 2166 q^{78} + 1116 q^{80} + 10728 q^{81} - 36 q^{82} - 30 q^{83} - 10 q^{85} - 8388 q^{86} - 138 q^{87} + 784 q^{88} - 26392 q^{90} - 96 q^{91} - 78 q^{92} + 25418 q^{93} - 42 q^{95} - 8924 q^{96} - 24 q^{97} + 48 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2205, [\chi])\) into newform subspaces

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