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Properties

Label 2475.4.ed
Level $2475$
Weight $4$
Character orbit 2475.ed
Rep. character $\chi_{2475}(169,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $8608$
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.ed (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2475 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 8672 8672 0
Cusp forms 8608 8608 0
Eisenstein series 64 64 0

Trace form

\( 8608 q - 5 q^{2} - 4289 q^{4} - 7 q^{5} - 60 q^{6} + 60 q^{8} + 46 q^{9} + O(q^{10}) \) \( 8608 q - 5 q^{2} - 4289 q^{4} - 7 q^{5} - 60 q^{6} + 60 q^{8} + 46 q^{9} - 3 q^{11} + 180 q^{12} - 5 q^{13} + 58 q^{14} - 24 q^{15} + 17031 q^{16} - 4 q^{19} - 531 q^{20} + 96 q^{21} - 5 q^{22} - 10 q^{23} - 132 q^{24} - 75 q^{25} + 40 q^{26} + 1470 q^{27} - 20 q^{28} + 695 q^{29} + 590 q^{30} - 55 q^{31} + 925 q^{33} + 2 q^{34} - 32 q^{35} - 620 q^{36} - 25 q^{38} + 111 q^{39} + 532 q^{40} - 1313 q^{41} + 1380 q^{42} - 316 q^{44} - 504 q^{45} + 40 q^{46} - 5 q^{47} - 330 q^{48} - 51554 q^{49} - 275 q^{50} + 42 q^{51} - 532 q^{54} + 346 q^{55} - 1242 q^{56} + 75 q^{58} + 326 q^{59} - 219 q^{60} - q^{61} + 1705 q^{63} + 134252 q^{64} - 456 q^{65} + 3716 q^{66} + 1520 q^{67} + 320 q^{68} + 371 q^{69} + 1688 q^{70} - 1864 q^{71} - 1735 q^{72} - 20 q^{73} + 2962 q^{74} - 838 q^{75} + 304 q^{76} - 2725 q^{77} + 4600 q^{78} + 750 q^{79} - 2792 q^{80} - 2274 q^{81} - 80 q^{82} - 1214 q^{84} + 997 q^{85} - 17 q^{86} - 20 q^{87} - 2565 q^{88} + 1656 q^{89} - 3534 q^{90} - 690 q^{91} - 85 q^{92} - 9225 q^{93} + 3210 q^{94} - 1994 q^{95} - 1384 q^{96} + 3390 q^{98} - 250 q^{99} + O(q^{100}) \)

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.