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Properties

Label 1225.4.l
Level $1225$
Weight $4$
Character orbit 1225.l
Rep. character $\chi_{1225}(176,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $1578$
Sturm bound $560$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1225.l (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(560\)

Dimensions

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

Total New Old
Modular forms 2556 1614 942
Cusp forms 2484 1578 906
Eisenstein series 72 36 36

Trace form

\( 1578 q + 5 q^{2} + 5 q^{3} - 1035 q^{4} - 39 q^{6} + 20 q^{7} + 31 q^{8} - 2238 q^{9} + O(q^{10}) \) \( 1578 q + 5 q^{2} + 5 q^{3} - 1035 q^{4} - 39 q^{6} + 20 q^{7} + 31 q^{8} - 2238 q^{9} + 83 q^{11} + 234 q^{12} - 25 q^{13} + 131 q^{14} - 4039 q^{16} + 141 q^{17} - 100 q^{18} - 468 q^{19} - 103 q^{21} + 213 q^{22} + 271 q^{23} + 1027 q^{24} + 151 q^{26} + 125 q^{27} + 132 q^{28} + 467 q^{29} - 1284 q^{31} - 559 q^{32} + 447 q^{33} + 709 q^{34} - 8433 q^{36} - 1185 q^{37} - 1595 q^{38} - 1373 q^{39} + 761 q^{41} - 755 q^{42} + 705 q^{43} - 593 q^{44} - 913 q^{46} - 93 q^{47} - 4240 q^{48} - 808 q^{49} - 1777 q^{51} + 291 q^{52} + 1125 q^{53} + 1184 q^{54} - 1780 q^{56} + 1064 q^{57} - 4225 q^{58} + 2523 q^{59} - 3507 q^{61} - 1945 q^{62} - 2126 q^{63} - 14877 q^{64} - 1137 q^{66} + 544 q^{67} + 8248 q^{68} + 3267 q^{69} + 643 q^{71} - 5632 q^{72} - 39 q^{73} + 3035 q^{74} - 4170 q^{76} + 1011 q^{77} - 2261 q^{78} - 2284 q^{79} - 28178 q^{81} + 314 q^{82} + 1069 q^{83} - 3820 q^{84} - 1795 q^{86} + 1033 q^{87} - 9325 q^{88} + 6797 q^{89} + 1257 q^{91} - 11066 q^{92} - 728 q^{93} + 4722 q^{94} + 7688 q^{96} + 11612 q^{97} - 7459 q^{98} - 10832 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1225, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)