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Properties

Label 1300.2.bg
Level $1300$
Weight $2$
Character orbit 1300.bg
Rep. character $\chi_{1300}(209,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $120$
Sturm bound $420$

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Defining parameters

Level: \( N \) \(=\) \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1300.bg (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(420\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1300, [\chi])\).

Total New Old
Modular forms 864 120 744
Cusp forms 816 120 696
Eisenstein series 48 0 48

Trace form

\( 120 q - 10 q^{5} + 26 q^{9} + O(q^{10}) \) \( 120 q - 10 q^{5} + 26 q^{9} - 10 q^{11} + 4 q^{15} + 10 q^{17} + 4 q^{19} + 4 q^{21} + 30 q^{23} + 28 q^{25} + 6 q^{29} + 24 q^{31} - 2 q^{35} - 16 q^{41} - 68 q^{45} - 40 q^{47} - 132 q^{49} - 12 q^{51} - 10 q^{53} - 52 q^{55} - 6 q^{59} - 20 q^{61} - 50 q^{63} + 2 q^{65} + 10 q^{67} - 22 q^{69} - 14 q^{71} + 40 q^{73} + 32 q^{75} + 40 q^{77} + 52 q^{79} - 52 q^{81} - 50 q^{83} + 10 q^{85} + 100 q^{87} + 32 q^{89} - 4 q^{91} - 2 q^{95} - 50 q^{97} - 80 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1300, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1300, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)