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Properties

Label 1225.4.u
Level $1225$
Weight $4$
Character orbit 1225.u
Rep. character $\chi_{1225}(116,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $2368$
Sturm bound $560$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1225.u (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(560\)

Dimensions

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

Total New Old
Modular forms 3424 2432 992
Cusp forms 3296 2368 928
Eisenstein series 128 64 64

Trace form

\( 2368 q + 3 q^{2} + 3 q^{3} + 1171 q^{4} + 8 q^{5} + 92 q^{6} + 134 q^{8} + 2595 q^{9} + O(q^{10}) \) \( 2368 q + 3 q^{2} + 3 q^{3} + 1171 q^{4} + 8 q^{5} + 92 q^{6} + 134 q^{8} + 2595 q^{9} + 11 q^{10} + 45 q^{11} + 95 q^{12} + 12 q^{13} - 682 q^{15} + 4531 q^{16} - 141 q^{17} - 142 q^{18} - 149 q^{19} - 316 q^{20} - 520 q^{22} + 391 q^{23} + 1010 q^{24} - 62 q^{25} + 1240 q^{26} + 360 q^{27} - 120 q^{29} - 1325 q^{30} + 45 q^{31} - 768 q^{32} - 405 q^{33} + 300 q^{34} - 20900 q^{36} + 603 q^{37} + 958 q^{38} - 1375 q^{39} + 413 q^{40} + 1612 q^{41} - 1064 q^{43} - 973 q^{44} - 709 q^{45} - 937 q^{46} - 421 q^{47} - 344 q^{48} + 266 q^{50} - 796 q^{51} - 1154 q^{52} - 2425 q^{53} - 1471 q^{54} - 690 q^{55} + 2796 q^{57} + 4283 q^{58} - 921 q^{59} - 5517 q^{60} - 1057 q^{61} + 116 q^{62} - 33274 q^{64} - 383 q^{65} - 2051 q^{66} + 1469 q^{67} + 698 q^{68} + 4176 q^{69} - 1324 q^{71} + 284 q^{72} + 1107 q^{73} + 398 q^{74} + 572 q^{75} - 14900 q^{76} - 9878 q^{78} + 835 q^{79} - 5348 q^{80} + 20861 q^{81} - 4880 q^{82} - 7672 q^{83} - 9914 q^{85} + 5419 q^{86} - 2491 q^{87} - 4252 q^{88} - 93 q^{89} + 1636 q^{90} + 8106 q^{92} + 9248 q^{93} - 1565 q^{94} + 1140 q^{95} - 833 q^{96} + 11256 q^{97} + 10216 q^{99} + O(q^{100}) \)

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

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