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Properties

Label 2205.4.eh
Level $2205$
Weight $4$
Character orbit 2205.eh
Rep. character $\chi_{2205}(73,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $10032$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2205.eh (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
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 24384 10128 14256
Cusp forms 24000 10032 13968
Eisenstein series 384 96 288

Trace form

\( 10032 q + 26 q^{2} + 46 q^{5} - 8 q^{7} + 72 q^{8} + O(q^{10}) \) \( 10032 q + 26 q^{2} + 46 q^{5} - 8 q^{7} + 72 q^{8} + 50 q^{10} + 80 q^{11} - 28 q^{13} - 13180 q^{16} + 326 q^{17} + 28 q^{20} + 788 q^{22} + 82 q^{23} + 86 q^{25} - 564 q^{26} - 1078 q^{28} - 336 q^{31} - 2502 q^{32} - 1036 q^{35} - 194 q^{37} - 2112 q^{38} - 2506 q^{40} + 504 q^{41} + 36 q^{43} - 6212 q^{46} + 58 q^{47} + 10184 q^{50} + 2684 q^{52} + 2266 q^{53} + 1064 q^{55} + 1212 q^{56} + 1638 q^{58} - 9440 q^{61} + 140 q^{62} - 898 q^{65} + 72 q^{67} - 6738 q^{68} - 9808 q^{70} + 264 q^{71} + 2426 q^{73} + 1736 q^{76} - 430 q^{77} + 5706 q^{80} + 6026 q^{82} + 12880 q^{83} + 3956 q^{85} - 2048 q^{86} - 3116 q^{88} - 4260 q^{91} - 4096 q^{92} - 3464 q^{95} - 36640 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{4}^{\mathrm{old}}(2205, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2205, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)