Properties

Label 1050.3.c
Level $1050$
Weight $3$
Character orbit 1050.c
Rep. character $\chi_{1050}(449,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $3$
Sturm bound $720$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(720\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1050, [\chi])\).

Total New Old
Modular forms 504 72 432
Cusp forms 456 72 384
Eisenstein series 48 0 48

Trace form

\( 72 q + 144 q^{4} - 48 q^{9} + O(q^{10}) \) \( 72 q + 144 q^{4} - 48 q^{9} + 288 q^{16} + 80 q^{19} + 56 q^{21} - 208 q^{31} - 96 q^{34} - 96 q^{36} + 104 q^{39} + 208 q^{46} - 504 q^{49} + 488 q^{51} + 288 q^{54} + 576 q^{64} + 32 q^{66} + 344 q^{69} + 160 q^{76} - 16 q^{79} - 336 q^{81} + 112 q^{84} - 336 q^{91} + 256 q^{94} - 648 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1050, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1050.3.c.a $8$ $28.610$ 8.0.157351936.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+2q^{4}+(-2+\cdots)q^{6}+\cdots\)
1050.3.c.b $32$ $28.610$ None \(0\) \(0\) \(0\) \(0\)
1050.3.c.c $32$ $28.610$ None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{3}^{\mathrm{old}}(1050, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)