Properties

Label 150.10.c
Level $150$
Weight $10$
Character orbit 150.c
Rep. character $\chi_{150}(49,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $11$
Sturm bound $300$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 150.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(300\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(150, [\chi])\).

Total New Old
Modular forms 282 26 256
Cusp forms 258 26 232
Eisenstein series 24 0 24

Trace form

\( 26 q - 6656 q^{4} - 2592 q^{6} - 170586 q^{9} - 143976 q^{11} - 129152 q^{14} + 1703936 q^{16} + 462596 q^{19} + 37260 q^{21} + 663552 q^{24} - 5139520 q^{26} - 20580516 q^{29} - 10091204 q^{31} + 19286208 q^{34}+ \cdots + 944626536 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(150, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
150.10.c.a 150.c 5.b $2$ $77.255$ \(\Q(\sqrt{-1}) \) None 150.10.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+16 i q^{2}+81 i q^{3}-256 q^{4}-1296 q^{6}+\cdots\)
150.10.c.b 150.c 5.b $2$ $77.255$ \(\Q(\sqrt{-1}) \) None 30.10.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-16 i q^{2}-81 i q^{3}-256 q^{4}-1296 q^{6}+\cdots\)
150.10.c.c 150.c 5.b $2$ $77.255$ \(\Q(\sqrt{-1}) \) None 30.10.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-16 i q^{2}-81 i q^{3}-256 q^{4}-1296 q^{6}+\cdots\)
150.10.c.d 150.c 5.b $2$ $77.255$ \(\Q(\sqrt{-1}) \) None 6.10.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+16 i q^{2}+81 i q^{3}-256 q^{4}-1296 q^{6}+\cdots\)
150.10.c.e 150.c 5.b $2$ $77.255$ \(\Q(\sqrt{-1}) \) None 30.10.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+16 i q^{2}+81 i q^{3}-256 q^{4}-1296 q^{6}+\cdots\)
150.10.c.f 150.c 5.b $2$ $77.255$ \(\Q(\sqrt{-1}) \) None 30.10.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+16 i q^{2}-81 i q^{3}-256 q^{4}+1296 q^{6}+\cdots\)
150.10.c.g 150.c 5.b $2$ $77.255$ \(\Q(\sqrt{-1}) \) None 150.10.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-16 i q^{2}+81 i q^{3}-256 q^{4}+1296 q^{6}+\cdots\)
150.10.c.h 150.c 5.b $2$ $77.255$ \(\Q(\sqrt{-1}) \) None 30.10.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-16 i q^{2}+81 i q^{3}-256 q^{4}+1296 q^{6}+\cdots\)
150.10.c.i 150.c 5.b $2$ $77.255$ \(\Q(\sqrt{-1}) \) None 30.10.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+16 i q^{2}-81 i q^{3}-256 q^{4}+1296 q^{6}+\cdots\)
150.10.c.j 150.c 5.b $4$ $77.255$ \(\Q(i, \sqrt{274})\) None 150.10.a.m \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2^{4}\beta _{1}q^{2}+3^{4}\beta _{1}q^{3}-2^{8}q^{4}-6^{4}q^{6}+\cdots\)
150.10.c.k 150.c 5.b $4$ $77.255$ \(\Q(i, \sqrt{6679})\) None 150.10.a.l \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2^{4}\beta _{1}q^{2}-3^{4}\beta _{1}q^{3}-2^{8}q^{4}+6^{4}q^{6}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(150, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)