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Properties

Label 1225.4.e
Level $1225$
Weight $4$
Character orbit 1225.e
Rep. character $\chi_{1225}(226,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $368$
Sturm bound $560$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1225.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(560\)

Dimensions

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

Total New Old
Modular forms 888 392 496
Cusp forms 792 368 424
Eisenstein series 96 24 72

Trace form

\( 368 q + q^{2} + 5 q^{3} - 723 q^{4} + 44 q^{6} + 18 q^{8} - 1595 q^{9} + O(q^{10}) \) \( 368 q + q^{2} + 5 q^{3} - 723 q^{4} + 44 q^{6} + 18 q^{8} - 1595 q^{9} - 25 q^{11} + 62 q^{12} + 20 q^{13} - 2563 q^{16} + 153 q^{17} - 7 q^{18} - 209 q^{19} + 972 q^{22} - 163 q^{23} - 468 q^{24} - 138 q^{26} - 910 q^{27} - 944 q^{29} - 483 q^{31} - 501 q^{32} + 355 q^{33} + 1052 q^{34} + 14150 q^{36} + 209 q^{37} - 194 q^{38} + 430 q^{39} + 236 q^{41} - 560 q^{43} - 402 q^{44} + 1296 q^{46} + 99 q^{47} - 60 q^{48} + 829 q^{51} + 612 q^{52} + 565 q^{53} + 1376 q^{54} + 1794 q^{57} - 2948 q^{58} - 315 q^{59} - 1483 q^{61} + 948 q^{62} + 17646 q^{64} - 842 q^{66} + 935 q^{67} + 4612 q^{68} - 1322 q^{69} + 3272 q^{71} + 2917 q^{72} + 2269 q^{73} - 296 q^{74} + 5532 q^{76} - 12424 q^{78} - 915 q^{79} - 8048 q^{81} - 2750 q^{82} - 3096 q^{83} - 990 q^{86} - 2090 q^{87} - 9152 q^{88} + 929 q^{89} + 8188 q^{92} - 55 q^{93} + 2776 q^{94} - 9434 q^{96} - 20 q^{97} + 1916 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1225, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)