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Properties

Label 2475.4.q
Level $2475$
Weight $4$
Character orbit 2475.q
Rep. character $\chi_{2475}(181,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $1792$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2475.q (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2475, [\chi])\).

Total New Old
Modular forms 4352 1808 2544
Cusp forms 4288 1792 2496
Eisenstein series 64 16 48

Trace form

\( 1792 q + q^{2} - 1785 q^{4} + 11 q^{5} - 14 q^{7} - 31 q^{8} + O(q^{10}) \) \( 1792 q + q^{2} - 1785 q^{4} + 11 q^{5} - 14 q^{7} - 31 q^{8} + 76 q^{10} - 39 q^{11} + 90 q^{13} - 31 q^{14} - 7005 q^{16} - 31 q^{17} - 141 q^{19} - 203 q^{20} + 508 q^{22} - 222 q^{23} + 45 q^{25} + 59 q^{26} + 183 q^{28} + 349 q^{29} + 191 q^{31} - 62 q^{32} - 14 q^{34} - 367 q^{35} + 263 q^{37} + 1511 q^{38} + 7 q^{40} + 705 q^{41} + 56 q^{43} + 41 q^{44} - 1201 q^{46} + 2934 q^{47} - 21040 q^{49} + 670 q^{50} + 1971 q^{52} + 1337 q^{53} + 502 q^{55} + 421 q^{56} + 566 q^{58} + 601 q^{59} + 4154 q^{61} - 86 q^{62} - 28645 q^{64} + 1185 q^{65} + 1380 q^{67} + 1787 q^{68} - 4257 q^{70} - 1781 q^{71} + 4595 q^{73} + 2033 q^{74} + 394 q^{76} - 2521 q^{77} - 1665 q^{79} - 1311 q^{80} + 7184 q^{82} + 75 q^{83} - 945 q^{85} - 1295 q^{86} - 4772 q^{88} - 2634 q^{89} + 1480 q^{91} + 8930 q^{92} - 4638 q^{94} + 109 q^{95} + 9215 q^{97} - 5122 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2475, [\chi]) \cong \)