Properties

Label 1050.3.h
Level $1050$
Weight $3$
Character orbit 1050.h
Rep. character $\chi_{1050}(349,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $3$
Sturm bound $720$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(720\)
Trace bound: \(1\)
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 48 456
Cusp forms 456 48 408
Eisenstein series 48 0 48

Trace form

\( 48 q - 96 q^{4} + 144 q^{9} + O(q^{10}) \) \( 48 q - 96 q^{4} + 144 q^{9} - 112 q^{11} - 32 q^{14} + 192 q^{16} + 12 q^{21} - 48 q^{29} - 288 q^{36} - 72 q^{39} + 224 q^{44} + 272 q^{46} - 148 q^{49} + 96 q^{51} + 64 q^{56} - 384 q^{64} + 608 q^{71} - 128 q^{74} + 736 q^{79} + 432 q^{81} - 24 q^{84} - 352 q^{86} - 188 q^{91} - 336 q^{99} + O(q^{100}) \)

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.h.a $8$ $28.610$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}-\zeta_{24}^{2}q^{3}-2q^{4}-\zeta_{24}^{7}q^{6}+\cdots\)
1050.3.h.b $16$ $28.610$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}-\beta _{3}q^{3}-2q^{4}+\beta _{11}q^{6}+\cdots\)
1050.3.h.c $24$ $28.610$ None \(0\) \(0\) \(0\) \(0\)

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

\( S_{3}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)