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Properties

Label 2450.2.bp
Level $2450$
Weight $2$
Character orbit 2450.bp
Rep. character $\chi_{2450}(13,\cdot)$
Character field $\Q(\zeta_{140})$
Dimension $6720$
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.bp (of order \(140\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1225 \)
Character field: \(\Q(\zeta_{140})\)
Sturm bound: \(840\)

Dimensions

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

Total New Old
Modular forms 20352 6720 13632
Cusp forms 19968 6720 13248
Eisenstein series 384 0 384

Trace form

\( 6720 q - 8 q^{7} + O(q^{10}) \) \( 6720 q - 8 q^{7} - 44 q^{15} - 280 q^{16} + 112 q^{17} + 20 q^{22} - 8 q^{23} + 8 q^{25} - 12 q^{28} + 24 q^{30} - 28 q^{35} - 280 q^{36} + 24 q^{37} + 112 q^{42} + 104 q^{43} + 448 q^{45} + 84 q^{47} + 32 q^{50} + 100 q^{53} - 84 q^{55} + 68 q^{57} + 80 q^{58} + 100 q^{63} + 32 q^{67} + 28 q^{70} + 84 q^{75} + 144 q^{77} + 80 q^{78} - 280 q^{81} + 840 q^{83} - 360 q^{84} - 40 q^{85} + 28 q^{87} + 8 q^{88} + 700 q^{89} - 336 q^{90} - 8 q^{92} - 20 q^{93} + 56 q^{95} + 32 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)