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Properties

Label 2205.2.p
Level $2205$
Weight $2$
Character orbit 2205.p
Rep. character $\chi_{2205}(1567,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $192$
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.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 736 208 528
Cusp forms 608 192 416
Eisenstein series 128 16 112

Trace form

\( 192 q - 4 q^{2} + 28 q^{8} + O(q^{10}) \) \( 192 q - 4 q^{2} + 28 q^{8} - 24 q^{11} - 176 q^{16} + 24 q^{22} - 44 q^{23} + 24 q^{25} + 92 q^{32} - 12 q^{43} + 40 q^{46} - 20 q^{50} - 16 q^{53} - 28 q^{58} + 72 q^{65} - 68 q^{67} + 88 q^{71} + 24 q^{85} + 104 q^{86} - 32 q^{88} - 68 q^{92} - 40 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2205, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)