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Properties

Label 2450.2.x
Level $2450$
Weight $2$
Character orbit 2450.x
Rep. character $\chi_{2450}(51,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1056$
Sturm bound $840$

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Defining parameters

Level: \( N \) \(=\) \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2450.x (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2450, [\chi])\).

Total New Old
Modular forms 5184 1056 4128
Cusp forms 4896 1056 3840
Eisenstein series 288 0 288

Trace form

\( 1056 q + 88 q^{4} + 14 q^{6} - 8 q^{7} + 102 q^{9} + O(q^{10}) \) \( 1056 q + 88 q^{4} + 14 q^{6} - 8 q^{7} + 102 q^{9} + 18 q^{11} + 4 q^{14} + 88 q^{16} + 18 q^{17} - 4 q^{18} + 10 q^{19} - 4 q^{21} + 14 q^{22} - 46 q^{23} + 6 q^{26} - 18 q^{27} + 4 q^{28} + 6 q^{29} + 20 q^{31} + 24 q^{33} + 16 q^{34} - 162 q^{36} + 8 q^{37} + 36 q^{38} + 88 q^{39} - 32 q^{41} + 74 q^{42} - 40 q^{43} - 24 q^{44} - 76 q^{46} + 36 q^{47} - 112 q^{49} - 104 q^{51} - 14 q^{52} + 126 q^{53} - 96 q^{54} - 24 q^{56} + 18 q^{57} + 116 q^{58} - 46 q^{59} + 24 q^{61} - 20 q^{62} - 6 q^{63} - 176 q^{64} + 4 q^{67} - 24 q^{68} - 76 q^{69} + 50 q^{71} - 4 q^{72} - 14 q^{73} + 6 q^{74} + 8 q^{76} - 50 q^{77} + 56 q^{78} + 8 q^{79} + 170 q^{81} + 16 q^{82} - 32 q^{83} + 14 q^{84} + 46 q^{86} + 102 q^{87} - 14 q^{88} + 92 q^{89} + 98 q^{91} + 8 q^{92} - 54 q^{93} + 66 q^{94} + 204 q^{97} - 4 q^{98} + 184 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)