Properties

Label 2394.4.a
Level $2394$
Weight $4$
Character orbit 2394.a
Rep. character $\chi_{2394}(1,\cdot)$
Character field $\Q$
Dimension $134$
Newform subspaces $36$
Sturm bound $1920$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2394.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 36 \)
Sturm bound: \(1920\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2394))\).

Total New Old
Modular forms 1456 134 1322
Cusp forms 1424 134 1290
Eisenstein series 32 0 32

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(7\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(6\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(11\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(11\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(12\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(12\)
Plus space\(+\)\(72\)
Minus space\(-\)\(62\)

Trace form

\( 134 q + 4 q^{2} + 536 q^{4} - 12 q^{5} + 16 q^{8} + O(q^{10}) \) \( 134 q + 4 q^{2} + 536 q^{4} - 12 q^{5} + 16 q^{8} + 40 q^{10} - 20 q^{11} + 20 q^{13} + 2144 q^{16} + 132 q^{17} - 48 q^{20} - 256 q^{23} + 2774 q^{25} - 72 q^{26} - 404 q^{29} + 1168 q^{31} + 64 q^{32} + 440 q^{34} + 140 q^{35} + 628 q^{37} + 160 q^{40} + 668 q^{41} - 228 q^{43} - 80 q^{44} - 48 q^{46} - 1200 q^{47} + 6566 q^{49} + 700 q^{50} + 80 q^{52} + 1244 q^{53} + 864 q^{55} + 384 q^{58} - 2656 q^{59} - 364 q^{61} - 368 q^{62} + 8576 q^{64} - 1400 q^{65} + 4256 q^{67} + 528 q^{68} + 1944 q^{71} + 1900 q^{73} + 2672 q^{74} + 616 q^{77} - 984 q^{79} - 192 q^{80} - 1688 q^{82} + 5536 q^{83} - 1944 q^{85} - 512 q^{86} + 4556 q^{89} - 1848 q^{91} - 1024 q^{92} - 1680 q^{94} + 5372 q^{97} + 196 q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2394))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 7 19
2394.4.a.a 2394.a 1.a $1$ $141.251$ \(\Q\) None \(-2\) \(0\) \(0\) \(7\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+7q^{7}-8q^{8}+42q^{11}+\cdots\)
2394.4.a.b 2394.a 1.a $1$ $141.251$ \(\Q\) None \(-2\) \(0\) \(10\) \(-7\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+10q^{5}-7q^{7}-8q^{8}+\cdots\)
2394.4.a.c 2394.a 1.a $1$ $141.251$ \(\Q\) None \(-2\) \(0\) \(10\) \(7\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+10q^{5}+7q^{7}-8q^{8}+\cdots\)
2394.4.a.d 2394.a 1.a $1$ $141.251$ \(\Q\) None \(2\) \(0\) \(-10\) \(-7\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}-10q^{5}-7q^{7}+8q^{8}+\cdots\)
2394.4.a.e 2394.a 1.a $1$ $141.251$ \(\Q\) None \(2\) \(0\) \(12\) \(7\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+12q^{5}+7q^{7}+8q^{8}+\cdots\)
2394.4.a.f 2394.a 1.a $2$ $141.251$ \(\Q(\sqrt{37}) \) None \(-4\) \(0\) \(4\) \(-14\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(1+2\beta )q^{5}-7q^{7}+\cdots\)
2394.4.a.g 2394.a 1.a $2$ $141.251$ \(\Q(\sqrt{13}) \) None \(-4\) \(0\) \(14\) \(14\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(5+4\beta )q^{5}+7q^{7}+\cdots\)
2394.4.a.h 2394.a 1.a $2$ $141.251$ \(\Q(\sqrt{2}) \) None \(-4\) \(0\) \(20\) \(14\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(10+3\beta )q^{5}+7q^{7}+\cdots\)
2394.4.a.i 2394.a 1.a $2$ $141.251$ \(\Q(\sqrt{85}) \) None \(4\) \(0\) \(-12\) \(-14\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(-5-2\beta )q^{5}-7q^{7}+\cdots\)
2394.4.a.j 2394.a 1.a $2$ $141.251$ \(\Q(\sqrt{5}) \) None \(4\) \(0\) \(-2\) \(14\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(1-4\beta )q^{5}+7q^{7}+\cdots\)
2394.4.a.k 2394.a 1.a $3$ $141.251$ 3.3.57553.1 None \(-6\) \(0\) \(-10\) \(-21\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(-3+\beta _{1})q^{5}-7q^{7}+\cdots\)
2394.4.a.l 2394.a 1.a $3$ $141.251$ 3.3.3221.1 None \(-6\) \(0\) \(0\) \(-21\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}-\beta _{2}q^{5}-7q^{7}-8q^{8}+\cdots\)
2394.4.a.m 2394.a 1.a $3$ $141.251$ 3.3.12092.1 None \(-6\) \(0\) \(20\) \(-21\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(7-\beta _{1})q^{5}-7q^{7}+\cdots\)
2394.4.a.n 2394.a 1.a $3$ $141.251$ 3.3.93944.1 None \(6\) \(0\) \(-10\) \(21\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(-3+\beta _{2})q^{5}+7q^{7}+\cdots\)
2394.4.a.o 2394.a 1.a $3$ $141.251$ 3.3.22397.1 None \(6\) \(0\) \(0\) \(-21\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}-\beta _{2}q^{5}-7q^{7}+8q^{8}+\cdots\)
2394.4.a.p 2394.a 1.a $3$ $141.251$ 3.3.42440.1 None \(6\) \(0\) \(20\) \(21\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(7+\beta _{1})q^{5}+7q^{7}+\cdots\)
2394.4.a.q 2394.a 1.a $4$ $141.251$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(0\) \(10\) \(-28\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(2-\beta _{1})q^{5}-7q^{7}+\cdots\)
2394.4.a.r 2394.a 1.a $4$ $141.251$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(0\) \(10\) \(28\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(2+\beta _{1})q^{5}+7q^{7}+\cdots\)
2394.4.a.s 2394.a 1.a $4$ $141.251$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(0\) \(-12\) \(28\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(-3+\beta _{1})q^{5}+7q^{7}+\cdots\)
2394.4.a.t 2394.a 1.a $4$ $141.251$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(0\) \(-10\) \(-28\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(-3-\beta _{2})q^{5}-7q^{7}+\cdots\)
2394.4.a.u 2394.a 1.a $4$ $141.251$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(0\) \(-10\) \(28\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(-2-\beta _{1})q^{5}+7q^{7}+\cdots\)
2394.4.a.v 2394.a 1.a $4$ $141.251$ 4.4.6939601.2 None \(8\) \(0\) \(-7\) \(-28\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(-2-2\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
2394.4.a.w 2394.a 1.a $4$ $141.251$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(0\) \(-7\) \(28\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(-2+\beta _{1}-\beta _{3})q^{5}+\cdots\)
2394.4.a.x 2394.a 1.a $4$ $141.251$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(0\) \(0\) \(-28\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}-\beta _{1}q^{5}-7q^{7}+8q^{8}+\cdots\)
2394.4.a.y 2394.a 1.a $4$ $141.251$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(0\) \(10\) \(-28\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(2+\beta _{1})q^{5}-7q^{7}+\cdots\)
2394.4.a.z 2394.a 1.a $5$ $141.251$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(0\) \(-21\) \(-35\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(-4+\beta _{1}+\beta _{4})q^{5}+\cdots\)
2394.4.a.ba 2394.a 1.a $5$ $141.251$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(0\) \(-21\) \(35\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(-4+\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
2394.4.a.bb 2394.a 1.a $5$ $141.251$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(0\) \(-20\) \(35\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(-4-\beta _{2})q^{5}+7q^{7}+\cdots\)
2394.4.a.bc 2394.a 1.a $5$ $141.251$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(0\) \(-8\) \(-35\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(-2+\beta _{2})q^{5}-7q^{7}+\cdots\)
2394.4.a.bd 2394.a 1.a $5$ $141.251$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(0\) \(8\) \(-35\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(2-\beta _{2})q^{5}-7q^{7}+\cdots\)
2394.4.a.be 2394.a 1.a $6$ $141.251$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-12\) \(0\) \(12\) \(42\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(2-\beta _{1})q^{5}+7q^{7}+\cdots\)
2394.4.a.bf 2394.a 1.a $6$ $141.251$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(0\) \(-12\) \(42\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(-2+\beta _{1})q^{5}+7q^{7}+\cdots\)
2394.4.a.bg 2394.a 1.a $7$ $141.251$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-14\) \(0\) \(-28\) \(49\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(-4+\beta _{2})q^{5}+7q^{7}+\cdots\)
2394.4.a.bh 2394.a 1.a $7$ $141.251$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-14\) \(0\) \(-18\) \(-49\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(-3+\beta _{1})q^{5}-7q^{7}+\cdots\)
2394.4.a.bi 2394.a 1.a $7$ $141.251$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(14\) \(0\) \(18\) \(-49\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(3-\beta _{1})q^{5}-7q^{7}+\cdots\)
2394.4.a.bj 2394.a 1.a $7$ $141.251$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(14\) \(0\) \(28\) \(49\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(4-\beta _{2})q^{5}+7q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2394))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2394)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(342))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(399))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(798))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1197))\)\(^{\oplus 2}\)