Properties

Label 2178.3.c
Level $2178$
Weight $3$
Character orbit 2178.c
Rep. character $\chi_{2178}(485,\cdot)$
Character field $\Q$
Dimension $74$
Newform subspaces $16$
Sturm bound $1188$
Trace bound $10$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2178 = 2 \cdot 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2178.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(1188\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2178, [\chi])\).

Total New Old
Modular forms 840 74 766
Cusp forms 744 74 670
Eisenstein series 96 0 96

Trace form

\( 74 q - 148 q^{4} + 8 q^{7} + O(q^{10}) \) \( 74 q - 148 q^{4} + 8 q^{7} - 20 q^{10} + 296 q^{16} + 48 q^{19} - 506 q^{25} - 16 q^{28} + 24 q^{31} + 4 q^{34} + 76 q^{37} + 40 q^{40} - 32 q^{43} + 16 q^{46} + 534 q^{49} - 172 q^{58} + 148 q^{61} - 592 q^{64} - 16 q^{67} - 16 q^{70} + 176 q^{73} - 96 q^{76} + 344 q^{79} + 188 q^{82} + 84 q^{85} - 656 q^{91} - 80 q^{94} - 880 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2178, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2178.3.c.a 2178.c 3.b $2$ $59.346$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-2q^{4}-5q^{7}-2\beta q^{8}-8q^{13}+\cdots\)
2178.3.c.b 2178.c 3.b $2$ $59.346$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-2q^{4}+3\beta q^{5}-2\beta q^{8}-6q^{10}+\cdots\)
2178.3.c.c 2178.c 3.b $2$ $59.346$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{2}-2q^{4}+3\beta q^{5}+2\beta q^{8}+6q^{10}+\cdots\)
2178.3.c.d 2178.c 3.b $2$ $59.346$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-2q^{4}+3\beta q^{5}+4q^{7}-2\beta q^{8}+\cdots\)
2178.3.c.e 2178.c 3.b $2$ $59.346$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{2}-2q^{4}+5q^{7}+2\beta q^{8}+8q^{13}+\cdots\)
2178.3.c.f 2178.c 3.b $4$ $59.346$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{3})q^{2}-2q^{4}+(-4\beta _{1}-\beta _{3})q^{5}+\cdots\)
2178.3.c.g 2178.c 3.b $4$ $59.346$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-2q^{4}+2\beta _{3}q^{5}+(-6+\beta _{2}+\cdots)q^{7}+\cdots\)
2178.3.c.h 2178.c 3.b $4$ $59.346$ \(\Q(\sqrt{-2}, \sqrt{-11})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-2q^{4}-\beta _{1}q^{5}-\beta _{2}q^{7}+2\beta _{1}q^{8}+\cdots\)
2178.3.c.i 2178.c 3.b $4$ $59.346$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(24\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-2q^{4}+2\beta _{3}q^{5}+(6-\beta _{2}+\cdots)q^{7}+\cdots\)
2178.3.c.j 2178.c 3.b $4$ $59.346$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(24\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{3})q^{2}-2q^{4}+(-4\beta _{1}-\beta _{3})q^{5}+\cdots\)
2178.3.c.k 2178.c 3.b $6$ $59.346$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-2q^{4}+\beta _{1}q^{5}+(-2+\beta _{5})q^{7}+\cdots\)
2178.3.c.l 2178.c 3.b $6$ $59.346$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-2q^{4}+\beta _{1}q^{5}+(2-\beta _{5})q^{7}+\cdots\)
2178.3.c.m 2178.c 3.b $8$ $59.346$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}-2q^{4}+(2\beta _{5}-2\beta _{6}+\beta _{7})q^{5}+\cdots\)
2178.3.c.n 2178.c 3.b $8$ $59.346$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}-2q^{4}+(\beta _{1}-\beta _{5}-2\beta _{7})q^{5}+\cdots\)
2178.3.c.o 2178.c 3.b $8$ $59.346$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}-2q^{4}+(\beta _{1}-\beta _{5}-2\beta _{7})q^{5}+\cdots\)
2178.3.c.p 2178.c 3.b $8$ $59.346$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{2}-2q^{4}+(2\beta _{5}-2\beta _{6}+\beta _{7})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(2178, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2178, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(726, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1089, [\chi])\)\(^{\oplus 2}\)