Properties

Label 150.4.c
Level $150$
Weight $4$
Character orbit 150.c
Rep. character $\chi_{150}(49,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $5$
Sturm bound $120$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 150.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(120\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(150, [\chi])\).

Total New Old
Modular forms 102 10 92
Cusp forms 78 10 68
Eisenstein series 24 0 24

Trace form

\( 10 q - 40 q^{4} + 12 q^{6} - 90 q^{9} + O(q^{10}) \) \( 10 q - 40 q^{4} + 12 q^{6} - 90 q^{9} - 168 q^{11} - 16 q^{14} + 160 q^{16} - 236 q^{19} + 132 q^{21} - 48 q^{24} + 376 q^{26} + 396 q^{29} - 916 q^{31} + 24 q^{34} + 360 q^{36} + 192 q^{39} - 132 q^{41} + 672 q^{44} + 864 q^{46} - 222 q^{49} - 468 q^{51} - 108 q^{54} + 64 q^{56} - 1320 q^{59} - 2368 q^{61} - 640 q^{64} + 1152 q^{66} + 504 q^{69} + 1152 q^{71} + 1160 q^{74} + 944 q^{76} + 352 q^{79} + 810 q^{81} - 528 q^{84} - 2000 q^{86} + 2772 q^{89} - 1940 q^{91} - 1152 q^{94} + 192 q^{96} + 1512 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(150, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
150.4.c.a $2$ $8.850$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}+3iq^{3}-4q^{4}-6q^{6}-2^{5}iq^{7}+\cdots\)
150.4.c.b $2$ $8.850$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}+3iq^{3}-4q^{4}-6q^{6}+23iq^{7}+\cdots\)
150.4.c.c $2$ $8.850$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-3iq^{3}-4q^{4}+6q^{6}-4iq^{7}+\cdots\)
150.4.c.d $2$ $8.850$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-3iq^{3}-4q^{4}+6q^{6}+2^{4}iq^{7}+\cdots\)
150.4.c.e $2$ $8.850$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-3iq^{3}-4q^{4}+6q^{6}+iq^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(150, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)