Properties

Label 2394.2.o
Level $2394$
Weight $2$
Character orbit 2394.o
Rep. character $\chi_{2394}(505,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $100$
Newform subspaces $24$
Sturm bound $960$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2394.o (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 24 \)
Sturm bound: \(960\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2394, [\chi])\).

Total New Old
Modular forms 992 100 892
Cusp forms 928 100 828
Eisenstein series 64 0 64

Trace form

\( 100 q - 2 q^{2} - 50 q^{4} + 4 q^{8} + O(q^{10}) \) \( 100 q - 2 q^{2} - 50 q^{4} + 4 q^{8} - 4 q^{11} - 16 q^{13} - 4 q^{14} - 50 q^{16} - 8 q^{17} + 2 q^{19} + 2 q^{22} + 4 q^{23} - 42 q^{25} + 8 q^{26} + 4 q^{29} - 16 q^{31} - 2 q^{32} + 12 q^{34} - 4 q^{35} - 8 q^{37} - 12 q^{38} - 34 q^{41} + 28 q^{43} + 2 q^{44} + 8 q^{46} - 44 q^{47} + 100 q^{49} + 36 q^{50} - 16 q^{52} + 12 q^{55} + 8 q^{56} + 24 q^{58} + 50 q^{59} + 8 q^{61} + 12 q^{62} + 100 q^{64} + 128 q^{65} - 34 q^{67} + 16 q^{68} + 8 q^{70} - 8 q^{71} - 22 q^{73} - 36 q^{74} + 2 q^{76} + 16 q^{77} - 14 q^{82} - 36 q^{83} + 36 q^{85} - 60 q^{86} - 4 q^{88} - 12 q^{89} + 4 q^{91} + 4 q^{92} - 16 q^{94} - 76 q^{95} - 6 q^{97} - 2 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2394, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2394.2.o.a 2394.o 19.c $2$ $19.116$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
2394.2.o.b 2394.o 19.c $2$ $19.116$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-3\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
2394.2.o.c 2394.o 19.c $2$ $19.116$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
2394.2.o.d 2394.o 19.c $2$ $19.116$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
2394.2.o.e 2394.o 19.c $2$ $19.116$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
2394.2.o.f 2394.o 19.c $2$ $19.116$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
2394.2.o.g 2394.o 19.c $2$ $19.116$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
2394.2.o.h 2394.o 19.c $2$ $19.116$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
2394.2.o.i 2394.o 19.c $2$ $19.116$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
2394.2.o.j 2394.o 19.c $2$ $19.116$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(3\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
2394.2.o.k 2394.o 19.c $4$ $19.116$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
2394.2.o.l 2394.o 19.c $4$ $19.116$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(-2\) \(0\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{4}-\beta _{1}q^{5}-q^{7}+\cdots\)
2394.2.o.m 2394.o 19.c $4$ $19.116$ \(\Q(\sqrt{-3}, \sqrt{73})\) None \(-2\) \(0\) \(6\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{2}-\beta _{2}q^{4}+(3-3\beta _{2}+\cdots)q^{5}+\cdots\)
2394.2.o.n 2394.o 19.c $4$ $19.116$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(0\) \(6\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+3\beta _{1}q^{5}+\cdots\)
2394.2.o.o 2394.o 19.c $4$ $19.116$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(0\) \(-6\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{1})q^{4}-3\beta _{1}q^{5}+\cdots\)
2394.2.o.p 2394.o 19.c $4$ $19.116$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(2\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1})q^{2}+\beta _{1}q^{4}+(-2-2\beta _{1}+\cdots)q^{5}+\cdots\)
2394.2.o.q 2394.o 19.c $4$ $19.116$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1})q^{2}+\beta _{1}q^{4}-\beta _{2}q^{5}+q^{7}+\cdots\)
2394.2.o.r 2394.o 19.c $6$ $19.116$ 6.0.45911232.1 None \(-3\) \(0\) \(-3\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{4})q^{2}-\beta _{4}q^{4}+(-1+\beta _{4}+\cdots)q^{5}+\cdots\)
2394.2.o.s 2394.o 19.c $6$ $19.116$ 6.0.591408.1 None \(3\) \(0\) \(-1\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{2}+(-1+\beta _{4})q^{4}+(-\beta _{1}+2\beta _{3}+\cdots)q^{5}+\cdots\)
2394.2.o.t 2394.o 19.c $6$ $19.116$ 6.0.70858800.1 None \(3\) \(0\) \(3\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1})q^{2}-\beta _{1}q^{4}+(1-\beta _{1})q^{5}+\cdots\)
2394.2.o.u 2394.o 19.c $6$ $19.116$ 6.0.45911232.1 None \(3\) \(0\) \(3\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{2}+(-1+\beta _{4})q^{4}+\beta _{4}q^{5}+q^{7}+\cdots\)
2394.2.o.v 2394.o 19.c $8$ $19.116$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(0\) \(1\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{4})q^{2}-\beta _{4}q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
2394.2.o.w 2394.o 19.c $10$ $19.116$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-5\) \(0\) \(-3\) \(-10\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{6}q^{2}+(-1+\beta _{6})q^{4}+(-\beta _{6}-\beta _{8}+\cdots)q^{5}+\cdots\)
2394.2.o.x 2394.o 19.c $10$ $19.116$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(5\) \(0\) \(3\) \(-10\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{6}q^{2}+(-1+\beta _{6})q^{4}+(\beta _{6}+\beta _{8}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2394, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)