Properties

Label 450.6.c
Level $450$
Weight $6$
Character orbit 450.c
Rep. character $\chi_{450}(199,\cdot)$
Character field $\Q$
Dimension $38$
Newform subspaces $17$
Sturm bound $540$
Trace bound $11$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 450.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(540\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(450, [\chi])\).

Total New Old
Modular forms 474 38 436
Cusp forms 426 38 388
Eisenstein series 48 0 48

Trace form

\( 38q - 608q^{4} + O(q^{10}) \) \( 38q - 608q^{4} - 1338q^{11} - 16q^{14} + 9728q^{16} - 4594q^{19} + 1600q^{26} + 17232q^{29} - 7532q^{31} + 2280q^{34} + 6270q^{41} + 21408q^{44} - 29904q^{46} - 172782q^{49} + 256q^{56} + 203640q^{59} + 43180q^{61} - 155648q^{64} - 231288q^{71} + 207056q^{74} + 73504q^{76} + 281300q^{79} - 16448q^{86} - 64266q^{89} - 240544q^{91} - 316032q^{94} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(450, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
450.6.c.a \(2\) \(72.173\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-4iq^{2}-2^{4}q^{4}+142iq^{7}+2^{6}iq^{8}+\cdots\)
450.6.c.b \(2\) \(72.173\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-2^{4}q^{4}+82iq^{7}-2^{5}iq^{8}+\cdots\)
450.6.c.c \(2\) \(72.173\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2iq^{2}-2^{4}q^{4}+74iq^{7}+2^{5}iq^{8}+\cdots\)
450.6.c.d \(2\) \(72.173\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2iq^{2}-2^{4}q^{4}+7^{2}iq^{7}+2^{5}iq^{8}+\cdots\)
450.6.c.e \(2\) \(72.173\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-4iq^{2}-2^{4}q^{4}+47iq^{7}+2^{6}iq^{8}+\cdots\)
450.6.c.f \(2\) \(72.173\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-2^{4}q^{4}+59iq^{7}-2^{5}iq^{8}+\cdots\)
450.6.c.g \(2\) \(72.173\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4iq^{2}-2^{4}q^{4}+79iq^{7}-2^{6}iq^{8}+\cdots\)
450.6.c.h \(2\) \(72.173\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2iq^{2}-2^{4}q^{4}+86iq^{7}+2^{5}iq^{8}+\cdots\)
450.6.c.i \(2\) \(72.173\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2iq^{2}-2^{4}q^{4}+2^{4}iq^{7}+2^{5}iq^{8}+\cdots\)
450.6.c.j \(2\) \(72.173\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2iq^{2}-2^{4}q^{4}+88iq^{7}+2^{5}iq^{8}+\cdots\)
450.6.c.k \(2\) \(72.173\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-4iq^{2}-2^{4}q^{4}+iq^{7}+2^{6}iq^{8}+\cdots\)
450.6.c.l \(2\) \(72.173\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-2^{4}q^{4}+7^{2}iq^{7}-2^{5}iq^{8}+\cdots\)
450.6.c.m \(2\) \(72.173\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-2^{4}q^{4}+74iq^{7}-2^{5}iq^{8}+\cdots\)
450.6.c.n \(2\) \(72.173\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4iq^{2}-2^{4}q^{4}+233iq^{7}-2^{6}iq^{8}+\cdots\)
450.6.c.o \(2\) \(72.173\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2iq^{2}-2^{4}q^{4}+11iq^{7}+2^{5}iq^{8}+\cdots\)
450.6.c.p \(4\) \(72.173\) \(\Q(i, \sqrt{4081})\) None \(0\) \(0\) \(0\) \(0\) \(q-4\beta _{1}q^{2}-2^{4}q^{4}+(-50\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
450.6.c.q \(4\) \(72.173\) \(\Q(i, \sqrt{4081})\) None \(0\) \(0\) \(0\) \(0\) \(q+4\beta _{1}q^{2}-2^{4}q^{4}+(-50\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(450, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(450, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)