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Properties

Label 2205.2.eh
Level $2205$
Weight $2$
Character orbit 2205.eh
Rep. character $\chi_{2205}(73,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $3312$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2205.eh (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2205, [\chi])\).

Total New Old
Modular forms 8256 3408 4848
Cusp forms 7872 3312 4560
Eisenstein series 384 96 288

Trace form

\( 3312 q + 26 q^{2} + 16 q^{5} - 26 q^{7} + O(q^{10}) \) \( 3312 q + 26 q^{2} + 16 q^{5} - 26 q^{7} - 10 q^{10} + 48 q^{11} - 28 q^{13} - 324 q^{16} + 54 q^{17} + 28 q^{20} - 8 q^{22} + 18 q^{23} - 24 q^{25} + 28 q^{26} + 42 q^{28} - 60 q^{31} + 138 q^{32} + 64 q^{35} - 20 q^{37} + 74 q^{40} + 112 q^{41} - 8 q^{43} + 108 q^{46} - 50 q^{47} - 136 q^{50} - 52 q^{52} + 106 q^{53} + 14 q^{55} + 192 q^{56} - 110 q^{58} - 96 q^{61} + 56 q^{62} + 32 q^{65} - 40 q^{67} + 162 q^{68} - 188 q^{70} + 128 q^{71} - 76 q^{73} + 56 q^{76} + 68 q^{77} + 6 q^{80} + 94 q^{82} + 42 q^{83} - 84 q^{85} + 92 q^{86} + 264 q^{88} + 28 q^{91} + 16 q^{92} - 54 q^{95} + 324 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2205, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2205, [\chi])\) into lower level spaces

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