Properties

Label 3150.3.c
Level $3150$
Weight $3$
Character orbit 3150.c
Rep. character $\chi_{3150}(449,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $6$
Sturm bound $2160$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3150.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(2160\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3150, [\chi])\).

Total New Old
Modular forms 1488 72 1416
Cusp forms 1392 72 1320
Eisenstein series 96 0 96

Trace form

\( 72 q + 144 q^{4} + O(q^{10}) \) \( 72 q + 144 q^{4} + 288 q^{16} - 160 q^{19} - 64 q^{31} - 48 q^{34} - 416 q^{46} - 504 q^{49} + 240 q^{61} + 576 q^{64} - 320 q^{76} + 128 q^{79} - 512 q^{94} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3150.3.c.a $8$ $85.831$ 8.0.157351936.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}+2q^{4}+\beta _{1}q^{7}-2\beta _{6}q^{8}+\cdots\)
3150.3.c.b $8$ $85.831$ 8.0.157351936.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+2q^{4}+\beta _{1}q^{7}-2\beta _{3}q^{8}+\cdots\)
3150.3.c.c $8$ $85.831$ 8.0.157351936.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+2q^{4}-\beta _{1}q^{7}+2\beta _{6}q^{8}+\cdots\)
3150.3.c.d $16$ $85.831$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+2q^{4}-\beta _{2}q^{7}-2\beta _{5}q^{8}+\cdots\)
3150.3.c.e $16$ $85.831$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+2q^{4}-\beta _{10}q^{7}+2\beta _{2}q^{8}+\cdots\)
3150.3.c.f $16$ $85.831$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}+2q^{4}+\beta _{2}q^{7}-2\beta _{6}q^{8}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)