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Properties

Label 1300.2.bw
Level $1300$
Weight $2$
Character orbit 1300.bw
Rep. character $\chi_{1300}(61,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $288$
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.bw (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(420\)

Dimensions

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

Total New Old
Modular forms 1728 288 1440
Cusp forms 1632 288 1344
Eisenstein series 96 0 96

Trace form

\( 288 q + 2 q^{5} + 40 q^{9} + O(q^{10}) \) \( 288 q + 2 q^{5} + 40 q^{9} + 14 q^{13} - 30 q^{15} - 2 q^{17} + 12 q^{19} - 2 q^{23} + 26 q^{25} - 24 q^{27} + 12 q^{29} + 12 q^{33} + 12 q^{35} - 3 q^{37} + 8 q^{39} - 15 q^{41} - 43 q^{45} + 18 q^{47} - 176 q^{49} + 20 q^{51} - 74 q^{53} - 17 q^{55} + 56 q^{57} + 6 q^{59} + 2 q^{61} + 11 q^{63} - q^{65} + 32 q^{67} - q^{69} - 16 q^{71} + 132 q^{73} - 13 q^{75} + 24 q^{77} + 8 q^{79} + 48 q^{81} - 50 q^{83} - 79 q^{85} + 38 q^{87} - 33 q^{89} - 26 q^{91} - 40 q^{93} - 30 q^{95} + 36 q^{97} + 40 q^{99} + O(q^{100}) \)

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

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