Properties

Label 150.11.b
Level $150$
Weight $11$
Character orbit 150.b
Rep. character $\chi_{150}(149,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $3$
Sturm bound $330$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 150.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(330\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(150, [\chi])\).

Total New Old
Modular forms 312 60 252
Cusp forms 288 60 228
Eisenstein series 24 0 24

Trace form

\( 60 q + 30720 q^{4} - 12160 q^{6} + 189620 q^{9} + O(q^{10}) \) \( 60 q + 30720 q^{4} - 12160 q^{6} + 189620 q^{9} + 15728640 q^{16} + 3053220 q^{19} - 4951780 q^{21} - 6225920 q^{24} - 145403220 q^{31} - 69960960 q^{34} + 97085440 q^{36} + 101713300 q^{39} - 1067228160 q^{46} - 2283165600 q^{49} + 2456240280 q^{51} - 1140828800 q^{54} - 150633660 q^{61} + 8053063680 q^{64} + 4371774720 q^{66} - 1171566120 q^{69} + 1563248640 q^{76} - 8764776120 q^{79} - 28079420780 q^{81} - 2535311360 q^{84} - 16602203100 q^{91} - 3775545600 q^{94} - 3187671040 q^{96} + 54274118280 q^{99} + O(q^{100}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(150, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
150.11.b.a $8$ $95.304$ 8.0.\(\cdots\).10 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(10\beta _{1}+3\beta _{3}-\beta _{4})q^{3}+2^{9}q^{4}+\cdots\)
150.11.b.b $24$ $95.304$ None \(0\) \(0\) \(0\) \(0\)
150.11.b.c $28$ $95.304$ None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{11}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(150, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)