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Properties

Label 1225.2.p
Level $1225$
Weight $2$
Character orbit 1225.p
Rep. character $\chi_{1225}(68,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $224$
Sturm bound $280$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1225.p (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1225, [\chi])\).

Total New Old
Modular forms 656 256 400
Cusp forms 464 224 240
Eisenstein series 192 32 160

Trace form

\( 224 q - 2 q^{2} - 6 q^{3} + 20 q^{8} + O(q^{10}) \) \( 224 q - 2 q^{2} - 6 q^{3} + 20 q^{8} + 28 q^{11} + 6 q^{12} + 108 q^{16} + 12 q^{17} + 36 q^{18} + 48 q^{22} + 14 q^{23} - 12 q^{26} - 12 q^{31} - 62 q^{32} - 224 q^{36} + 8 q^{37} - 12 q^{38} + 4 q^{43} - 4 q^{46} + 24 q^{47} - 28 q^{51} + 24 q^{52} - 24 q^{53} + 72 q^{57} - 70 q^{58} - 72 q^{61} - 204 q^{66} - 22 q^{67} - 12 q^{68} + 80 q^{71} + 8 q^{72} - 24 q^{73} - 120 q^{78} + 116 q^{81} - 6 q^{82} - 4 q^{86} + 18 q^{87} + 16 q^{88} - 28 q^{92} + 48 q^{93} - 60 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1225, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1225, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1225, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)