Properties

Label 90.6.c
Level $90$
Weight $6$
Character orbit 90.c
Rep. character $\chi_{90}(19,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $4$
Sturm bound $108$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 90.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(108\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(90, [\chi])\).

Total New Old
Modular forms 98 12 86
Cusp forms 82 12 70
Eisenstein series 16 0 16

Trace form

\( 12 q - 192 q^{4} - 6 q^{5} + O(q^{10}) \) \( 12 q - 192 q^{4} - 6 q^{5} + 408 q^{10} + 948 q^{11} - 384 q^{14} + 3072 q^{16} + 7464 q^{19} + 96 q^{20} + 4416 q^{25} + 2640 q^{26} - 10692 q^{29} + 23472 q^{31} + 10800 q^{34} + 34116 q^{35} - 6528 q^{40} - 7200 q^{41} - 15168 q^{44} + 3984 q^{46} + 12612 q^{49} + 29952 q^{50} - 85728 q^{55} + 6144 q^{56} - 183540 q^{59} - 86400 q^{61} - 49152 q^{64} + 132492 q^{65} + 4272 q^{70} + 88248 q^{71} - 164016 q^{74} - 119424 q^{76} - 136800 q^{79} - 1536 q^{80} - 38676 q^{85} + 230928 q^{86} - 245904 q^{89} - 6456 q^{91} + 268272 q^{94} + 241800 q^{95} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(90, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
90.6.c.a \(2\) \(14.435\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-110\) \(0\) \(q+2iq^{2}-2^{4}q^{4}+(-55+5i)q^{5}+\cdots\)
90.6.c.b \(2\) \(14.435\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(110\) \(0\) \(q+2iq^{2}-2^{4}q^{4}+(55+5i)q^{5}+2iq^{7}+\cdots\)
90.6.c.c \(4\) \(14.435\) \(\Q(i, \sqrt{1249})\) None \(0\) \(0\) \(-6\) \(0\) \(q+\beta _{1}q^{2}-2^{4}q^{4}+(-1-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
90.6.c.d \(4\) \(14.435\) \(\Q(i, \sqrt{19})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{2}q^{2}-2^{4}q^{4}+(5\beta _{1}-15\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(90, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(90, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)