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Properties

Label 1225.4.bn
Level $1225$
Weight $4$
Character orbit 1225.bn
Rep. character $\chi_{1225}(82,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $6000$
Sturm bound $560$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1225.bn (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(560\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1225, [\chi])\).

Total New Old
Modular forms 10224 6096 4128
Cusp forms 9936 6000 3936
Eisenstein series 288 96 192

Trace form

\( 6000 q + 26 q^{2} + 22 q^{3} + 56 q^{6} + 32 q^{7} - 96 q^{8} + O(q^{10}) \) \( 6000 q + 26 q^{2} + 22 q^{3} + 56 q^{6} + 32 q^{7} - 96 q^{8} - 108 q^{11} + 70 q^{12} + 28 q^{13} - 7972 q^{16} - 570 q^{17} + 34 q^{18} + 280 q^{21} + 892 q^{22} - 30 q^{23} + 1172 q^{26} + 28 q^{27} - 938 q^{28} + 456 q^{31} + 2874 q^{32} + 1090 q^{33} + 31672 q^{36} + 194 q^{37} + 1932 q^{38} - 952 q^{41} - 2150 q^{42} - 708 q^{43} + 12268 q^{46} - 14 q^{47} + 8684 q^{51} - 2684 q^{52} + 2266 q^{53} - 12120 q^{56} - 3834 q^{57} - 6342 q^{58} + 4492 q^{61} + 140 q^{62} - 3116 q^{63} - 1092 q^{66} + 1944 q^{67} + 2106 q^{68} - 488 q^{71} + 17334 q^{72} + 4198 q^{73} + 1736 q^{76} + 6170 q^{77} - 7604 q^{78} - 73968 q^{81} + 6166 q^{82} - 12432 q^{83} - 10748 q^{86} - 2468 q^{87} - 916 q^{88} + 15120 q^{91} + 3688 q^{92} + 21184 q^{93} + 38692 q^{96} + 41316 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1225, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1225, [\chi])\) into lower level spaces

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