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Properties

Label 2205.2.cs
Level $2205$
Weight $2$
Character orbit 2205.cs
Rep. character $\chi_{2205}(46,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1128$
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.cs (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 4128 1128 3000
Cusp forms 3936 1128 2808
Eisenstein series 192 0 192

Trace form

\( 1128 q + 96 q^{4} - 2 q^{5} - 6 q^{7} + O(q^{10}) \) \( 1128 q + 96 q^{4} - 2 q^{5} - 6 q^{7} + 2 q^{10} - 2 q^{11} - 16 q^{13} + 62 q^{14} + 96 q^{16} - 12 q^{17} + 4 q^{19} + 20 q^{20} - 16 q^{22} + 48 q^{23} + 94 q^{25} - 10 q^{26} + 98 q^{28} + 42 q^{29} - 8 q^{31} + 12 q^{34} - 10 q^{35} + 102 q^{37} + 80 q^{38} + 6 q^{40} + 16 q^{41} + 28 q^{43} + 68 q^{44} + 66 q^{46} + 128 q^{47} - 46 q^{49} - 196 q^{52} + 48 q^{53} - 24 q^{55} + 206 q^{56} - 118 q^{58} + 26 q^{59} - 60 q^{61} + 56 q^{62} - 304 q^{64} - 6 q^{65} - 18 q^{67} + 160 q^{68} - 14 q^{70} - 56 q^{71} - 10 q^{73} + 2 q^{74} + 48 q^{76} + 30 q^{77} - 10 q^{79} + 76 q^{80} + 138 q^{82} - 30 q^{83} + 4 q^{85} + 204 q^{86} - 34 q^{88} + 92 q^{89} + 290 q^{91} + 60 q^{92} + 370 q^{94} - 4 q^{95} + 136 q^{97} + 42 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2205, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)