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Properties

Label 1225.4.ba
Level $1225$
Weight $4$
Character orbit 1225.ba
Rep. character $\chi_{1225}(79,\cdot)$
Character field $\Q(\zeta_{30})$
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.ba (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 2368 q + 5 q^{2} + 5 q^{3} - 1165 q^{4} + 8 q^{5} - 68 q^{6} - 250 q^{8} - 2589 q^{9} + O(q^{10}) \) \( 2368 q + 5 q^{2} + 5 q^{3} - 1165 q^{4} + 8 q^{5} - 68 q^{6} - 250 q^{8} - 2589 q^{9} - 27 q^{10} - 39 q^{11} + 5 q^{12} + 20 q^{13} + 618 q^{15} + 4563 q^{16} - 315 q^{17} - 149 q^{19} + 604 q^{20} - 1480 q^{22} + 585 q^{23} + 1054 q^{24} - 186 q^{25} - 1224 q^{26} - 1300 q^{27} - 120 q^{29} - 293 q^{30} - 39 q^{31} + 805 q^{33} + 236 q^{34} - 18380 q^{36} + 5 q^{37} + 1250 q^{38} - 1267 q^{39} + 679 q^{40} - 1588 q^{41} - 941 q^{44} - 1095 q^{45} + 943 q^{46} + 5 q^{47} - 60 q^{48} + 3798 q^{50} + 812 q^{51} - 2310 q^{52} - 855 q^{53} - 1115 q^{54} - 722 q^{55} - 6835 q^{58} - 921 q^{59} - 7327 q^{60} + 1063 q^{61} - 8380 q^{62} + 35430 q^{64} - 1773 q^{65} + 1193 q^{66} - 2305 q^{67} + 3960 q^{69} + 1276 q^{71} + 3990 q^{72} + 2285 q^{73} + 526 q^{74} - 1772 q^{75} + 15476 q^{76} - 310 q^{78} + 835 q^{79} + 9054 q^{80} + 21913 q^{81} - 6760 q^{83} + 530 q^{85} - 5413 q^{86} + 5 q^{87} - 8610 q^{88} - 93 q^{89} - 20976 q^{90} - 5590 q^{92} - 1629 q^{94} + 6156 q^{95} - 793 q^{96} + 13040 q^{97} + 10000 q^{99} + O(q^{100}) \)

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

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