Properties

Label 5915.2.a
Level $5915$
Weight $2$
Character orbit 5915.a
Rep. character $\chi_{5915}(1,\cdot)$
Character field $\Q$
Dimension $310$
Newform subspaces $42$
Sturm bound $1456$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 5915 = 5 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5915.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 42 \)
Sturm bound: \(1456\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5915))\).

Total New Old
Modular forms 756 310 446
Cusp forms 701 310 391
Eisenstein series 55 0 55

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

\(5\)\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(37\)
\(+\)\(+\)\(-\)\(-\)\(42\)
\(+\)\(-\)\(+\)\(-\)\(40\)
\(+\)\(-\)\(-\)\(+\)\(36\)
\(-\)\(+\)\(+\)\(-\)\(47\)
\(-\)\(+\)\(-\)\(+\)\(30\)
\(-\)\(-\)\(+\)\(+\)\(30\)
\(-\)\(-\)\(-\)\(-\)\(48\)
Plus space\(+\)\(133\)
Minus space\(-\)\(177\)

Trace form

\( 310q - 4q^{2} - 4q^{3} + 304q^{4} + 4q^{6} - 2q^{7} + 300q^{9} + O(q^{10}) \) \( 310q - 4q^{2} - 4q^{3} + 304q^{4} + 4q^{6} - 2q^{7} + 300q^{9} - 4q^{10} - 2q^{11} - 2q^{14} - 2q^{15} + 284q^{16} - 12q^{17} - 8q^{18} - 24q^{19} + 2q^{21} - 20q^{22} + 16q^{23} + 16q^{24} + 310q^{25} + 20q^{27} - 14q^{28} + 2q^{29} + 20q^{30} + 4q^{31} + 16q^{32} - 36q^{33} - 4q^{34} + 4q^{35} + 292q^{36} - 24q^{37} + 16q^{38} - 24q^{40} - 28q^{41} + 4q^{42} - 12q^{43} + 36q^{44} + 8q^{45} + 8q^{46} + 28q^{47} + 40q^{48} + 310q^{49} - 4q^{50} - 6q^{51} - 12q^{53} + 44q^{54} + 8q^{55} - 6q^{56} - 20q^{57} + 52q^{58} + 36q^{59} - 4q^{60} - 40q^{61} + 64q^{62} - 18q^{63} + 300q^{64} + 100q^{66} - 44q^{67} + 48q^{68} + 36q^{69} - 2q^{70} - 16q^{71} + 80q^{72} - 80q^{73} + 88q^{74} - 4q^{75} + 10q^{79} + 32q^{80} + 270q^{81} + 88q^{82} - 32q^{83} + 36q^{84} - 14q^{85} + 64q^{86} + 28q^{87} + 32q^{88} + 48q^{89} + 88q^{92} + 36q^{93} + 36q^{94} + 20q^{95} + 144q^{96} - 20q^{97} - 4q^{98} + 60q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5915))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 7 13
5915.2.a.a \(1\) \(47.232\) \(\Q\) None \(-2\) \(0\) \(1\) \(-1\) \(-\) \(+\) \(+\) \(q-2q^{2}+2q^{4}+q^{5}-q^{7}-3q^{9}-2q^{10}+\cdots\)
5915.2.a.b \(1\) \(47.232\) \(\Q\) None \(-2\) \(1\) \(1\) \(-1\) \(-\) \(+\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}-q^{7}+\cdots\)
5915.2.a.c \(1\) \(47.232\) \(\Q\) None \(-2\) \(3\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(q-2q^{2}+3q^{3}+2q^{4}-q^{5}-6q^{6}+\cdots\)
5915.2.a.d \(1\) \(47.232\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{4}+q^{5}+q^{7}+3q^{8}-3q^{9}+\cdots\)
5915.2.a.e \(1\) \(47.232\) \(\Q\) None \(-1\) \(1\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
5915.2.a.f \(1\) \(47.232\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{3}-2q^{4}+q^{5}-q^{7}-2q^{9}+3q^{11}+\cdots\)
5915.2.a.g \(1\) \(47.232\) \(\Q\) None \(1\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{4}-q^{5}+q^{7}-3q^{8}-3q^{9}+\cdots\)
5915.2.a.h \(1\) \(47.232\) \(\Q\) None \(1\) \(1\) \(1\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
5915.2.a.i \(1\) \(47.232\) \(\Q\) None \(2\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(q+2q^{2}+2q^{4}-q^{5}+q^{7}-3q^{9}-2q^{10}+\cdots\)
5915.2.a.j \(1\) \(47.232\) \(\Q\) None \(2\) \(1\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}+q^{7}+\cdots\)
5915.2.a.k \(1\) \(47.232\) \(\Q\) None \(2\) \(3\) \(1\) \(-1\) \(-\) \(+\) \(+\) \(q+2q^{2}+3q^{3}+2q^{4}+q^{5}+6q^{6}+\cdots\)
5915.2.a.l \(2\) \(47.232\) \(\Q(\sqrt{17}) \) None \(1\) \(-1\) \(-2\) \(2\) \(+\) \(-\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{3}+(2+\beta )q^{4}-q^{5}+\cdots\)
5915.2.a.m \(4\) \(47.232\) 4.4.1957.1 None \(-3\) \(4\) \(-4\) \(4\) \(+\) \(-\) \(+\) \(q+(-1-\beta _{1}-\beta _{2})q^{2}+(1-\beta _{2}-\beta _{3})q^{3}+\cdots\)
5915.2.a.n \(4\) \(47.232\) 4.4.12197.1 None \(1\) \(0\) \(4\) \(4\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
5915.2.a.o \(5\) \(47.232\) 5.5.36497.1 None \(0\) \(-3\) \(-5\) \(-5\) \(+\) \(+\) \(+\) \(q+(\beta _{1}-\beta _{3}+\beta _{4})q^{2}+(\beta _{2}+\beta _{4})q^{3}+\cdots\)
5915.2.a.p \(5\) \(47.232\) 5.5.36497.1 None \(0\) \(-3\) \(5\) \(5\) \(-\) \(-\) \(+\) \(q+(-\beta _{1}+\beta _{3}-\beta _{4})q^{2}+(\beta _{2}+\beta _{4})q^{3}+\cdots\)
5915.2.a.q \(5\) \(47.232\) 5.5.81589.1 None \(0\) \(-2\) \(-5\) \(5\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
5915.2.a.r \(5\) \(47.232\) 5.5.81589.1 None \(0\) \(-2\) \(5\) \(-5\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
5915.2.a.s \(5\) \(47.232\) 5.5.144209.1 None \(0\) \(-1\) \(-5\) \(-5\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}-q^{5}+(-\beta _{3}+\cdots)q^{6}+\cdots\)
5915.2.a.t \(5\) \(47.232\) 5.5.144209.1 None \(0\) \(-1\) \(5\) \(5\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+q^{5}+(\beta _{3}+\cdots)q^{6}+\cdots\)
5915.2.a.u \(6\) \(47.232\) 6.6.45853772.1 None \(-3\) \(0\) \(-6\) \(-6\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\cdots\)
5915.2.a.v \(6\) \(47.232\) 6.6.3728753.1 None \(-2\) \(-1\) \(6\) \(-6\) \(-\) \(+\) \(+\) \(q+\beta _{5}q^{2}+(-1-\beta _{1}-\beta _{2}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
5915.2.a.w \(6\) \(47.232\) 6.6.3728753.1 None \(2\) \(-1\) \(-6\) \(6\) \(+\) \(-\) \(-\) \(q-\beta _{5}q^{2}+(\beta _{1}+\beta _{4})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
5915.2.a.x \(7\) \(47.232\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(0\) \(-7\) \(7\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
5915.2.a.y \(7\) \(47.232\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-1\) \(-7\) \(7\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5915.2.a.z \(7\) \(47.232\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-1\) \(7\) \(-7\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5915.2.a.ba \(7\) \(47.232\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(7\) \(-7\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(2+\beta _{1}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
5915.2.a.bb \(7\) \(47.232\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(1\) \(0\) \(7\) \(-7\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2})q^{4}+q^{5}+\cdots\)
5915.2.a.bc \(9\) \(47.232\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(2\) \(-9\) \(-9\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5915.2.a.bd \(9\) \(47.232\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(2\) \(9\) \(9\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5915.2.a.be \(10\) \(47.232\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-4\) \(-10\) \(10\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{3}+\beta _{6}+\beta _{9})q^{4}+\cdots\)
5915.2.a.bf \(10\) \(47.232\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-4\) \(10\) \(-10\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{3}+\beta _{6}+\beta _{9})q^{4}+\cdots\)
5915.2.a.bg \(15\) \(47.232\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-7\) \(-7\) \(15\) \(15\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
5915.2.a.bh \(15\) \(47.232\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-2\) \(-6\) \(-15\) \(15\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}+\beta _{14}q^{3}+(2-\beta _{10}+\beta _{11}+\cdots)q^{4}+\cdots\)
5915.2.a.bi \(15\) \(47.232\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-1\) \(5\) \(15\) \(-15\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5915.2.a.bj \(15\) \(47.232\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(1\) \(5\) \(-15\) \(15\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5915.2.a.bk \(15\) \(47.232\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(2\) \(-6\) \(15\) \(-15\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+\beta _{14}q^{3}+(2-\beta _{10}+\beta _{11}+\cdots)q^{4}+\cdots\)
5915.2.a.bl \(15\) \(47.232\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(7\) \(-7\) \(-15\) \(-15\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
5915.2.a.bm \(18\) \(47.232\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(4\) \(-18\) \(-18\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5915.2.a.bn \(18\) \(47.232\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(4\) \(18\) \(18\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5915.2.a.bo \(21\) \(47.232\) None \(-4\) \(5\) \(-21\) \(-21\) \(+\) \(+\) \(+\)
5915.2.a.bp \(21\) \(47.232\) None \(4\) \(5\) \(21\) \(21\) \(-\) \(-\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5915))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5915)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(455))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(845))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1183))\)\(^{\oplus 2}\)