Properties

Label 2394.2.a
Level $2394$
Weight $2$
Character orbit 2394.a
Rep. character $\chi_{2394}(1,\cdot)$
Character field $\Q$
Dimension $46$
Newform subspaces $29$
Sturm bound $960$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2394.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 29 \)
Sturm bound: \(960\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2394))\).

Total New Old
Modular forms 496 46 450
Cusp forms 465 46 419
Eisenstein series 31 0 31

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.
\(+\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(18\)
Minus space\(-\)\(28\)

Trace form

\( 46 q + 2 q^{2} + 46 q^{4} - 4 q^{5} + 2 q^{8} + O(q^{10}) \) \( 46 q + 2 q^{2} + 46 q^{4} - 4 q^{5} + 2 q^{8} + 4 q^{10} - 4 q^{11} + 12 q^{13} + 46 q^{16} + 12 q^{17} - 4 q^{20} + 78 q^{25} + 12 q^{26} + 4 q^{29} + 2 q^{32} - 4 q^{34} - 4 q^{35} + 12 q^{37} + 4 q^{40} + 28 q^{41} - 12 q^{43} - 4 q^{44} - 24 q^{46} + 8 q^{47} + 46 q^{49} + 14 q^{50} + 12 q^{52} + 12 q^{53} + 8 q^{55} - 8 q^{58} + 24 q^{59} + 12 q^{61} + 8 q^{62} + 46 q^{64} + 16 q^{65} + 16 q^{67} + 12 q^{68} - 24 q^{71} - 68 q^{73} - 8 q^{77} - 16 q^{79} - 4 q^{80} + 20 q^{82} - 32 q^{83} + 32 q^{85} - 36 q^{89} + 16 q^{91} - 8 q^{94} + 36 q^{97} + 2 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2394))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7 19
2394.2.a.a \(1\) \(19.116\) \(\Q\) None \(-1\) \(0\) \(-4\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-4q^{5}+q^{7}-q^{8}+4q^{10}+\cdots\)
2394.2.a.b \(1\) \(19.116\) \(\Q\) None \(-1\) \(0\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots\)
2394.2.a.c \(1\) \(19.116\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-6q^{11}+2q^{13}+\cdots\)
2394.2.a.d \(1\) \(19.116\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+2q^{13}-q^{14}+\cdots\)
2394.2.a.e \(1\) \(19.116\) \(\Q\) None \(-1\) \(0\) \(2\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\)
2394.2.a.f \(1\) \(19.116\) \(\Q\) None \(-1\) \(0\) \(4\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}+4q^{5}-q^{7}-q^{8}-4q^{10}+\cdots\)
2394.2.a.g \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(-4\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-4q^{5}+q^{7}+q^{8}-4q^{10}+\cdots\)
2394.2.a.h \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(-2\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots\)
2394.2.a.i \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}-4q^{13}+\cdots\)
2394.2.a.j \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-6q^{11}-4q^{13}+\cdots\)
2394.2.a.k \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{13}+q^{14}+\cdots\)
2394.2.a.l \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+6q^{11}+2q^{13}+\cdots\)
2394.2.a.m \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(2\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots\)
2394.2.a.n \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(2\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}+2q^{10}+\cdots\)
2394.2.a.o \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(4\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+4q^{5}+q^{7}+q^{8}+4q^{10}+\cdots\)
2394.2.a.p \(2\) \(19.116\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-2\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+(-1-\beta )q^{5}+q^{7}-q^{8}+\cdots\)
2394.2.a.q \(2\) \(19.116\) \(\Q(\sqrt{13}) \) None \(-2\) \(0\) \(-1\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}-\beta q^{5}+q^{7}-q^{8}+\beta q^{10}+\cdots\)
2394.2.a.r \(2\) \(19.116\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots\)
2394.2.a.s \(2\) \(19.116\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(2\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{7}-q^{8}+\cdots\)
2394.2.a.t \(2\) \(19.116\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(4\) \(2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\)
2394.2.a.u \(2\) \(19.116\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-4\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots\)
2394.2.a.v \(2\) \(19.116\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}+(-1-\beta )q^{5}-q^{7}+q^{8}+\cdots\)
2394.2.a.w \(2\) \(19.116\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+(1-3\beta )q^{5}+q^{7}+q^{8}+\cdots\)
2394.2.a.x \(2\) \(19.116\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+\beta q^{5}-q^{7}+q^{8}+\beta q^{10}+\cdots\)
2394.2.a.y \(2\) \(19.116\) \(\Q(\sqrt{29}) \) None \(2\) \(0\) \(1\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+\beta q^{5}-q^{7}+q^{8}+\beta q^{10}+\cdots\)
2394.2.a.z \(2\) \(19.116\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(2\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+(1+\beta )q^{5}+q^{7}+q^{8}+\cdots\)
2394.2.a.ba \(3\) \(19.116\) 3.3.469.1 None \(-3\) \(0\) \(-5\) \(-3\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}+(-2+\beta _{1})q^{5}-q^{7}-q^{8}+\cdots\)
2394.2.a.bb \(3\) \(19.116\) 3.3.148.1 None \(-3\) \(0\) \(-2\) \(-3\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+(-1-\beta _{1})q^{5}-q^{7}-q^{8}+\cdots\)
2394.2.a.bc \(3\) \(19.116\) 3.3.148.1 None \(3\) \(0\) \(2\) \(-3\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}+(1+\beta _{1})q^{5}-q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2394))\) into lower level spaces

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