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Properties

Label 2205.4.cv
Level $2205$
Weight $4$
Character orbit 2205.cv
Rep. character $\chi_{2205}(118,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $5016$
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.cv (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 12192 5064 7128
Cusp forms 12000 5016 6984
Eisenstein series 192 48 144

Trace form

\( 5016 q + 10 q^{2} + 14 q^{5} - 28 q^{7} - 42 q^{8} + O(q^{10}) \) \( 5016 q + 10 q^{2} + 14 q^{5} - 28 q^{7} - 42 q^{8} - 14 q^{10} + 76 q^{11} - 14 q^{13} + 13276 q^{16} - 434 q^{17} + 14 q^{20} - 818 q^{22} + 122 q^{23} + 214 q^{25} + 1092 q^{26} - 62 q^{28} + 1914 q^{32} + 496 q^{35} - 346 q^{37} + 126 q^{38} - 14 q^{40} + 252 q^{41} - 66 q^{43} - 1756 q^{46} + 98 q^{47} - 10112 q^{50} - 14 q^{52} - 1390 q^{53} - 1106 q^{55} + 3300 q^{56} - 3738 q^{58} - 6076 q^{61} - 98 q^{62} - 1838 q^{65} + 144 q^{67} + 9754 q^{70} - 204 q^{71} - 14 q^{73} - 1820 q^{76} - 1658 q^{77} - 12194 q^{82} + 6146 q^{83} - 3986 q^{85} - 4180 q^{86} - 3052 q^{88} - 276 q^{91} + 4126 q^{92} - 3220 q^{95} - 7748 q^{98} + O(q^{100}) \)

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

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