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Properties

Label 3675.2.ba
Level $3675$
Weight $2$
Character orbit 3675.ba
Rep. character $\chi_{3675}(589,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $816$
Sturm bound $1120$

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Defining parameters

Level: \( N \) \(=\) \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3675.ba (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1120\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3675, [\chi])\).

Total New Old
Modular forms 2304 816 1488
Cusp forms 2176 816 1360
Eisenstein series 128 0 128

Trace form

\( 816 q + 202 q^{4} + 4 q^{5} - 2 q^{6} + 30 q^{8} + 204 q^{9} + O(q^{10}) \) \( 816 q + 202 q^{4} + 4 q^{5} - 2 q^{6} + 30 q^{8} + 204 q^{9} - 8 q^{10} + 6 q^{11} + 4 q^{15} - 210 q^{16} - 10 q^{17} + 14 q^{19} - 8 q^{20} - 70 q^{22} + 20 q^{23} - 24 q^{24} - 18 q^{25} + 12 q^{26} - 8 q^{29} + 12 q^{30} - 6 q^{31} + 10 q^{33} + 12 q^{34} - 202 q^{36} - 10 q^{37} - 30 q^{38} - 8 q^{39} + 26 q^{40} + 22 q^{41} + 58 q^{44} - 4 q^{45} + 40 q^{47} - 128 q^{50} - 32 q^{51} - 40 q^{52} + 170 q^{53} + 2 q^{54} + 2 q^{55} + 130 q^{58} - 36 q^{59} + 14 q^{60} - 32 q^{61} + 110 q^{62} + 220 q^{64} - 2 q^{65} + 80 q^{67} + 4 q^{69} - 40 q^{71} + 30 q^{72} + 60 q^{73} - 12 q^{74} + 16 q^{75} + 104 q^{76} + 4 q^{79} + 44 q^{80} - 204 q^{81} - 70 q^{83} - 64 q^{85} - 84 q^{86} + 40 q^{87} + 120 q^{88} + 18 q^{89} - 22 q^{90} + 190 q^{92} + 26 q^{94} - 124 q^{95} + 6 q^{96} - 100 q^{97} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3675, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3675, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3675, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)