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Properties

Label 1225.4.o
Level $1225$
Weight $4$
Character orbit 1225.o
Rep. character $\chi_{1225}(344,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1208$
Sturm bound $560$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1225.o (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(560\)

Dimensions

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

Total New Old
Modular forms 1712 1248 464
Cusp forms 1648 1208 440
Eisenstein series 64 40 24

Trace form

\( 1208 q + 5 q^{2} + 5 q^{3} + 1187 q^{4} + 31 q^{5} + 7 q^{6} + 80 q^{8} + 2645 q^{9} + O(q^{10}) \) \( 1208 q + 5 q^{2} + 5 q^{3} + 1187 q^{4} + 31 q^{5} + 7 q^{6} + 80 q^{8} + 2645 q^{9} - 11 q^{10} + 5 q^{11} - 155 q^{12} + 5 q^{13} + 165 q^{15} - 4417 q^{16} + 165 q^{17} + 43 q^{19} + 337 q^{20} - 710 q^{22} - 75 q^{23} - 612 q^{24} + 247 q^{25} + 474 q^{26} - 55 q^{27} + 65 q^{29} + 1257 q^{30} - 561 q^{31} + 325 q^{33} - 181 q^{34} - 10015 q^{36} - 1500 q^{37} + 2755 q^{38} + 617 q^{39} - 1064 q^{40} - 479 q^{41} + 170 q^{44} - 1095 q^{45} - 961 q^{46} - 85 q^{47} + 1500 q^{48} + 371 q^{50} - 1046 q^{51} - 1740 q^{52} + 3450 q^{53} + 1621 q^{54} - 1441 q^{55} + 2620 q^{58} + 501 q^{59} - 1554 q^{60} - 637 q^{61} + 1530 q^{62} + 17994 q^{64} - 1808 q^{65} - 3460 q^{66} - 415 q^{67} - 91 q^{69} - 1047 q^{71} + 10415 q^{72} + 3725 q^{73} + 6328 q^{74} - 1325 q^{75} - 468 q^{76} + 9545 q^{78} - 1059 q^{79} + 7514 q^{80} - 21121 q^{81} + 2165 q^{83} - 3382 q^{85} + 1957 q^{86} - 8475 q^{87} - 6990 q^{88} + 3812 q^{89} + 1097 q^{90} - 9100 q^{92} + 6751 q^{94} - 6379 q^{95} - 2496 q^{96} - 7825 q^{97} + 3032 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1225, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)